Download or read book Orlicz Spaces and Generalized Orlicz Spaces written by Petteri Harjulehto and published by Springer. This book was released on 2019-05-07 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
Download or read book Generalized Orlicz Spaces and Related PDE written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Weighted Inequalities In Lorentz And Orlicz Spaces written by Vakhtang Kokilashvili and published by World Scientific. This book was released on 1991-12-31 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a survey of latest results on weighted inequalities in Lorentz, Orlicz spaces and Zygmund classes. During the last few years they have become one of the mostdeveloped offshoots of the theory of the harmonic analysis operators. Up to now there has been no monograph devoted to these questions, the results are mostly scattered in various journals and a part of the book consists of results not published anywhere else. Many of theorems presented have only previously been published in Russian.
Download or read book Orlicz Spaces and Modular Spaces written by J. Musielak and published by Springer. This book was released on 2006-11-14 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Maximal Function on Musie ak Orlicz Spaces and Generalized Lebesgue Spaces written by Lars Diening and published by . This book was released on 2003 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Partial Differential Equations in Anisotropic Musielak Orlicz Spaces written by Iwona Chlebicka and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed study of nonlinear partial differential equations satisfying certain nonstandard growth conditions which simultaneously extend polynomial, inhomogeneous and fully anisotropic growth. The common property of the many different kinds of equations considered is that the growth conditions of the highest order operators lead to a formulation of the equations in Musielak-Orlicz spaces. This high level of generality, understood as full anisotropy and inhomogeneity, requires new proof concepts and a generalization of the formalism, calling for an extended functional analytic framework. This theory is established in the first part of the book, which serves as an introduction to the subject, but is also an important ingredient of the whole story. The second part uses these theoretical tools for various types of PDEs, including abstract and parabolic equations but also PDEs arising from fluid and solid mechanics. For connoisseurs, there is a short chapter on homogenization of elliptic PDEs. The book will be of interest to researchers working in PDEs and in functional analysis.
Download or read book Applications Of Orlicz Spaces written by M.M. Rao and published by CRC Press. This book was released on 2002-02-08 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents previously unpublished material on the fundumental pronciples and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes. Provides practical applications in statistics and probability.
Download or read book Lebesgue and Sobolev Spaces with Variable Exponents written by Lars Diening and published by Springer. This book was released on 2011-03-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of variable exponent function spaces has witnessed an explosive growth in recent years. The standard reference article for basic properties is already 20 years old. Thus this self-contained monograph collecting all the basic properties of variable exponent Lebesgue and Sobolev spaces is timely and provides a much-needed accessible reference work utilizing consistent notation and terminology. Many results are also provided with new and improved proofs. The book also presents a number of applications to PDE and fluid dynamics.
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 Real Variable Theory of Musielak Orlicz Hardy Spaces written by Dachun Yang and published by Springer. This book was released on 2017-05-09 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this book is to give a detailed and complete survey of recent progress related to the real-variable theory of Musielak–Orlicz Hardy-type function spaces, and to lay the foundations for further applications. The real-variable theory of function spaces has always been at the core of harmonic analysis. Recently, motivated by certain questions in analysis, some more general Musielak–Orlicz Hardy-type function spaces were introduced. These spaces are defined via growth functions which may vary in both the spatial variable and the growth variable. By selecting special growth functions, the resulting spaces may have subtler and finer structures, which are necessary in order to solve various endpoint or sharp problems. This book is written for graduate students and researchers interested in function spaces and, in particular, Hardy-type spaces.
Download or read book Orlicz spaces and modular spaces written by and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis on Function Spaces of Musielak Orlicz Type written by Osvaldo Mendez and published by CRC Press. This book was released on 2019-01-21 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis on Function Spaces of Musielak-Orlicz Type provides a state-of-the-art survey on the theory of function spaces of Musielak-Orlicz type. The book also offers readers a step-by-step introduction to the theory of Musielak–Orlicz spaces, and introduces associated function spaces, extending up to the current research on the topic Musielak-Orlicz spaces came under renewed interest when applications to electrorheological hydrodynamics forced the particular case of the variable exponent Lebesgue spaces on to center stage. Since then, research efforts have typically been oriented towards carrying over the results of classical analysis into the framework of variable exponent function spaces. In recent years it has been suggested that many of the fundamental results in the realm of variable exponent Lebesgue spaces depend only on the intrinsic structure of the Musielak-Orlicz function, thus opening the door for a unified theory which encompasses that of Lebesgue function spaces with variable exponent. Features Gives a self-contained, concise account of the basic theory, in such a way that even early-stage graduate students will find it useful Contains numerous applications Facilitates the unified treatment of seemingly different theoretical and applied problems Includes a number of open problems in the area
Download or read book Characterizations of Orlicz Sobolev spaces in terms of generalized Orlicz Poincar inequalities written by Toni Heikkinen and published by . This book was released on 2006 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Optimization in Function Spaces written by Peter Kosmol and published by Walter de Gruyter. This book was released on 2011-02-28 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus
Download or read book Riesz Thorin Theorem in Generalized Orlicz Spaces of Nonsymmetric Type written by H. Hudzik and published by . This book was released on 1980 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Function Spaces 1 written by Luboš Pick and published by Walter de Gruyter. This book was released on 2012-12-19 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first part of the second revised and extended edition of the well established book "Function Spaces" by Alois Kufner, Oldřich John, and Svatopluk Fučík. Like the first edition this monograph is an introduction to function spaces defined in terms of differentiability and integrability classes. It provides a catalogue of various spaces and benefits as a handbook for those who use function spaces in their research or lecture courses. This first volume is devoted to the study of function spaces, based on intrinsic properties of a function such as its size, continuity, smoothness, various forms of a control over the mean oscillation, and so on. The second volume will be dedicated to the study of function spaces of Sobolev type, in which the key notion is the weak derivative of a function of several variables.
Download or read book Nonexpansive Maps in Generalized Orlicz Spaces written by Enrique Lami Dozo and published by . This book was released on 1986 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
