Orlicz Spaces and Generalized Orlicz Spaces
Orlicz Spaces and Generalized Orlicz Spaces

Author: Petteri Harjulehto

Publisher: Springer

Published: 2019-05-07

Total Pages: 169

ISBN-13: 303015100X

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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.

Weighted Inequalities In Lorentz And Orlicz Spaces
Weighted Inequalities In Lorentz And Orlicz Spaces

Author: Vakhtang Kokilashvili

Publisher: World Scientific

Published: 1991-12-31

Total Pages: 248

ISBN-13: 9814506281

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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.

Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces
Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces

Author: Iwona Chlebicka

Publisher:

Published: 2021

Total Pages: 0

ISBN-13: 9783030888572

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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.

Applications Of Orlicz Spaces
Applications Of Orlicz Spaces

Author: M.M. Rao

Publisher: CRC Press

Published: 2002-02-08

Total Pages: 496

ISBN-13: 9780203910863

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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.

Real-Variable Theory of Musielak-Orlicz Hardy Spaces
Real-Variable Theory of Musielak-Orlicz Hardy Spaces

Author: Dachun Yang

Publisher: Springer

Published: 2017-05-09

Total Pages: 476

ISBN-13: 331954361X

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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.

Lebesgue and Sobolev Spaces with Variable Exponents
Lebesgue and Sobolev Spaces with Variable Exponents

Author: Lars Diening

Publisher: Springer

Published: 2011-03-29

Total Pages: 516

ISBN-13: 3642183638

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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.

Morrey Spaces
Morrey Spaces

Author: Yoshihiro Sawano

Publisher: CRC Press

Published: 2020-09-16

Total Pages: 316

ISBN-13: 1000064077

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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