Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-17 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume I focused mainly on harmonic analysis. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-16 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Download or read book Morrey Spaces written by David Adams and published by Birkhäuser. This book was released on 2015-12-31 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any “full” interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.

Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-09-16 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume I focused mainly on harmonic analysis. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Download or read book Weighted Morrey Spaces written by Marcus Laurel and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-02 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a testament to the potency of the method of singular integrals of layer potential type in solving boundary value problems for weakly elliptic systems in the setting of Muckenhoupt-weighted Morrey spaces and their pre-duals. A functional analytic framework for Muckenhoupt-weighted Morrey spaces in the rough setting of Ahlfors regular sets is built from the ground up and subsequently supports a Calderón-Zygmund theory on this brand of Morrey space in the optimal geometric environment of uniformly rectifiable sets. A thorough duality theory for such Morrey spaces is also developed and ushers in a never-before-seen Calderón-Zygmund theory for Muckenhoupt-weighted Block spaces. Both weighted Morrey and Block spaces are also considered through the lens of (generalized) Banach function spaces, and ultimately, a variety of boundary value problems are formulated and solved with boundary data arbitrarily prescribed from either scale of space. The fairly self-contained nature of this monograph ensures that graduate students, researchers, and professionals in a variety of fields, e.g., function space theory, harmonic analysis, and PDE, will find this monograph a welcome and valuable addition to the mathematical literature.

Download or read book Morrey and Campanato Meet Besov Lizorkin and Triebel written by Wen Yuan and published by Springer Science & Business Media. This book was released on 2010-09-18 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last 60 years the theory of function spaces has been a subject of growing interest and increasing diversity. Based on three formally different developments, namely, the theory of Besov and Triebel-Lizorkin spaces, the theory of Morrey and Campanato spaces and the theory of Q spaces, the authors develop a unified framework for all of these spaces. As a byproduct, the authors provide a completion of the theory of Triebel-Lizorkin spaces when p = ∞.

Download or read book Harmonic Analysis written by Satoru Igari and published by . This book was released on 1991 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: G. Alexopoulos: Parabolic Harnack inequalities and Riesz transforms on Lie groups of polynomial growth.- H. Arai: Harmonic analysis with respect to degenerate Laplacian on strictly pseudoconvex domains.- J.M. Ash, R. Brown: Uniqueness and nonuniqueness for harmonic functions with zero nontangential limits.- A. Carbery, E. Hernndez, F. Soria: Estimates for the Kakeya maximal operator on radial functions in Rn.- S.-Y.A. Chang, P.C. Yang: Spectral invariants of conformal metrics.- M. Christ: Remarks on the breakdown of analycity for b and Szeg kernels.- R. Coifman, S. Semmes: L2 estimates in nonlinear Fourier analysis.- Dinh Dung: On optimal recovery of multivariate periodic functions.- S.A.A. Emara: A class of weighted inequalities.- G.I. Gaudry: Some singular integrals on the affine group.- J.-P. Kahane: From Riesz products to random sets.- T. Kawazoe: A model of reduction in harmonic analysis on real rank 1 semisimple Lie groups I.- P.G. Lemari: Wavelets, spline interpolation and Lie groups.- P. Mattila: Principle values of Cauchy integrals, rectifiable measures and sets.- A. Miyachi: Extension theorems for real variable Hardy and Hardy-Sobolev spaces.- T. Mizuhara: Boundedness of some classical operators on generalized Morrey spaces.- G. Sinnamon: Interpolation of spaces defined by the level function.- T.N. Varopoulos: Groups of superpolynomial growth.- J.M. Wilson: Littlewood-Paley theory in one and two parameters.- J.M. Wilson: Two-weight norm inequalities for the Fourier transform.- Program.- List of participants.

Download or read book Morrey Spaces written by Yoshihiro Sawano and published by CRC Press. This book was released on 2020-06-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with focus on harmonic analysis in volume I and generalizations and interpolation of Morrey spaces in volume II. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Download or read book MSCEIS 2019 written by Lala Septem Riza and published by European Alliance for Innovation. This book was released on 2020-07-30 with total page 1652 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 7th Mathematics, Science, and Computer Science Education International Seminar (MSCEIS) was held by the Faculty of Mathematics and Natural Science Education, Universitas Pendidikan Indonesia (UPI) and the collaboration with 12 University associated in Asosiasi MIPA LPTK Indonesia (AMLI) consisting of Universitas Negeri Semarang (UNNES), Universitas Pendidikan Indonesia (UPI), Universitas Negeri Yogyakarta (UNY), Universitas Negeri Malang (UM), Universitas Negeri Jakarta (UNJ), Universitas Negeri Medan (UNIMED), Universitas Negeri Padang (UNP), Universitas Negeri Manado (UNIMA), Universitas Negeri Makassar (UNM), Universitas Pendidikan Ganesha (UNDHIKSA), Universitas Negeri Gorontalo (UNG), and Universitas Negeri Surabaya (UNESA). In this year, MSCEIS 2019 takes the following theme: "Mathematics, Science, and Computer Science Education for Addressing Challenges and Implementations of Revolution-Industry 4.0" held on October 12, 2019 in Bandung, West Java, Indonesia.

Download or read book Real Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko written by Yinqin Li and published by Springer Nature. This book was released on 2023-02-14 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: The real-variable theory of function spaces has always been at the core of harmonic analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of harmonic analysis, with applications and connections to complex analysis, partial differential equations, and functional analysis. This book is devoted to exploring properties of generalized Herz spaces and establishing a complete real-variable theory of Hardy spaces associated with local and global generalized Herz spaces via a totally fresh perspective. This means that the authors view these generalized Herz spaces as special cases of ball quasi-Banach function spaces. In this book, the authors first give some basic properties of generalized Herz spaces and obtain the boundedness and the compactness characterizations of commutators on them. Then the authors introduce the associated Herz–Hardy spaces, localized Herz–Hardy spaces, and weak Herz–Hardy spaces, and develop a complete real-variable theory of these Herz–Hardy spaces, including their various maximal function, atomic, molecular as well as various Littlewood–Paley function characterizations. As applications, the authors establish the boundedness of some important operators arising from harmonic analysis on these Herz–Hardy spaces. Finally, the inhomogeneous Herz–Hardy spaces and their complete real-variable theory are also investigated. With the fresh perspective and the improved conclusions on the real-variable theory of Hardy spaces associated with ball quasi-Banach function spaces, all the obtained results of this book are new and their related exponents are sharp. This book will be appealing to researchers and graduate students who are interested in function spaces and their applications.

Download or read book Topics in Contemporary Mathematical Analysis and Applications written by Hemen Dutta and published by CRC Press. This book was released on 2020-12-22 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems This book is written for individual researchers, educators, students, and department libraries.

Download or read book Operator Theory Pseudo Differential Equations and Mathematical Physics written by Yuri I. Karlovich and published by Springer Science & Business Media. This book was released on 2012-10-30 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers devoted to the 70th birthday of Professor Vladimir Rabinovich. The opening article (by Stefan Samko) includes a short biography of Vladimir Rabinovich, along with some personal recollections and bibliography of his work. It is followed by twenty research and survey papers in various branches of analysis (pseudodifferential operators and partial differential equations, Toeplitz, Hankel, and convolution type operators, variable Lebesgue spaces, etc.) close to Professor Rabinovich's research interests. Many of them are written by participants of the International workshop “Analysis, Operator Theory, and Mathematical Physics” (Ixtapa, Mexico, January 23–27, 2012) having a long history of scientific collaboration with Vladimir Rabinovich, and are partially based on the talks presented there.The volume will be of great interest to researchers and graduate students in differential equations, operator theory, functional and harmonic analysis, and mathematical physics.​

Download or read book Theory of Besov Spaces written by Yoshihiro Sawano and published by Springer. This book was released on 2018-11-04 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.

Download or read book Advanced Topics in Mathematical Analysis written by Michael Ruzhansky and published by CRC Press. This book was released on 2019-01-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.

Download or read book Function Spaces and Inequalities written by Pankaj Jain and published by Springer. This book was released on 2017-10-20 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev–Besov and Triebel–Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11–15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.

Download or read book Modern Methods in Operator Theory and Harmonic Analysis written by Alexey Karapetyants and published by Springer Nature. This book was released on 2019-08-28 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis – all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.

Download or read book The Navier Stokes Equations written by Hermann Sohr and published by Springer Science & Business Media. This book was released on 2012-12-13 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers’ convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, operators, etc. Another important objective is to formulate the theory for a completely general domain ?. In particular, the theory applies to arbitrary unbounded, non-smooth domains. For this reason, in the nonlinear case, we have to restrict ourselves to space dimensions n=2,3 that are also most signi?cant from the physical point of view. For mathematical generality, we will develop the l- earized theory for all n? 2. Although the functional-analytic approach developed here is, in principle, known to specialists, its systematic treatment is not available, and even the diverseaspectsavailablearespreadoutintheliterature.However,theliterature is very wide, and I did not even try to include a full list of related papers, also because this could be confusing for the student. In this regard, I would like to apologize for not quoting all the works that, directly or indirectly, have inspired this monograph.