Orlicz Spaces And Generalized Orlicz Spaces

Author : Petteri Harjulehto,Peter Hästö
Publisher : Springer
Page : 169 pages
File Size : 41,8 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9783030151003

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Orlicz Spaces and Generalized Orlicz Spaces by Petteri Harjulehto,Peter Hästö Pdf

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.

Author : Iwona Chlebicka,Piotr Gwiazda,Agnieszka Świerczewska-Gwiazda,Aneta Wróblewska-Kamińska
Publisher : Springer Nature
Page : 389 pages
File Size : 55,6 Mb
Release : 2021-11-01
Category : Mathematics
ISBN : 9783030888565

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Partial Differential Equations in Anisotropic Musielak-Orlicz Spaces by Iwona Chlebicka,Piotr Gwiazda,Agnieszka Świerczewska-Gwiazda,Aneta Wróblewska-Kamińska Pdf

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.

Author : J. Musielak
Publisher : Springer
Page : 227 pages
File Size : 41,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540386926

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Orlicz Spaces and Modular Spaces by J. Musielak Pdf

Author : M.M. Rao,Z.D. Ren
Publisher : CRC Press
Page : 496 pages
File Size : 52,6 Mb
Release : 2002-02-08
Category : Mathematics
ISBN : 0203910869

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Applications Of Orlicz Spaces by M.M. Rao,Z.D. Ren Pdf

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.

Author : Vakhtang Mikha?lovich Kokilashvili,Miroslav Krbec
Publisher : World Scientific
Page : 250 pages
File Size : 41,9 Mb
Release : 1991
Category : Mathematics
ISBN : 9810206127

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Weighted Inequalities in Lorentz and Orlicz Spaces by Vakhtang Mikha?lovich Kokilashvili,Miroslav Krbec Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,5 Mb
Release : 1983
Category : Electronic
ISBN : 0387127062

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Orlicz spaces and modular spaces by Anonim Pdf

Author : Lars Diening,Petteri Harjulehto,Peter Hästö,Michael Ruzicka
Publisher : Springer
Page : 509 pages
File Size : 47,7 Mb
Release : 2011-03-29
Category : Mathematics
ISBN : 9783642183638

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Lebesgue and Sobolev Spaces with Variable Exponents by Lars Diening,Petteri Harjulehto,Peter Hästö,Michael Ruzicka Pdf

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.

Author : Dachun Yang,Yiyu Liang,Luong Dang Ky
Publisher : Springer
Page : 476 pages
File Size : 53,8 Mb
Release : 2017-05-09
Category : Mathematics
ISBN : 9783319543611

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Real-Variable Theory of Musielak-Orlicz Hardy Spaces by Dachun Yang,Yiyu Liang,Luong Dang Ky Pdf

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.

Author : Jan Lang,Osvaldo Mendez
Publisher : CRC Press
Page : 262 pages
File Size : 49,8 Mb
Release : 2018-12-13
Category : Function spaces
ISBN : 1498762603

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Analysis on Function Spaces of Musielak-Orlicz Type by Jan Lang,Osvaldo Mendez Pdf

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

Author : M.M. Rao,Z.D. Ren
Publisher : CRC Press
Page : 472 pages
File Size : 53,6 Mb
Release : 1991-03-14
Category : Mathematics
ISBN : 0824784782

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Theory of Orlicz SPates by M.M. Rao,Z.D. Ren Pdf

A reference/text for mathematicians or students involved in analysis, differential equations, probability theory, and the study of integral operators where only Lebesgue spaces were used in the past. Updates and extends the pioneering work by Krasnosel'skii and Rutickii in their 1958 treatise on Orl

Author : Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim
Publisher : CRC Press
Page : 316 pages
File Size : 40,8 Mb
Release : 2020-09-16
Category : Mathematics
ISBN : 9781000064070

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Morrey Spaces by Yoshihiro Sawano,Giuseppe Di Fazio,Denny Ivanal Hakim Pdf

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

Author : Mark Aleksandrovich Krasnoselʹskiĭ
Publisher : Unknown
Page : 224 pages
File Size : 44,6 Mb
Release : 1960
Category : Convex domains
ISBN : MINN:31951D03778752X

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Convex Functions and Orlicz Spaces by Mark Aleksandrovich Krasnoselʹskiĭ Pdf

Author : Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Publisher : Springer Nature
Page : 585 pages
File Size : 41,6 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030774936

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Operator Theory and Harmonic Analysis by Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek Pdf

This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.

Author : David V. Cruz-Uribe,Alberto Fiorenza
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 42,9 Mb
Release : 2013-02-12
Category : Mathematics
ISBN : 9783034805483

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Variable Lebesgue Spaces by David V. Cruz-Uribe,Alberto Fiorenza Pdf

This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.​

Author : Wolfram Bauer,Roland Duduchava,Sergei Grudsky,Marinus A. Kaashoek
Publisher : Springer Nature
Page : 467 pages
File Size : 53,7 Mb
Release : 2020-09-01
Category : Mathematics
ISBN : 9783030446512

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Operator Algebras, Toeplitz Operators and Related Topics by Wolfram Bauer,Roland Duduchava,Sergei Grudsky,Marinus A. Kaashoek Pdf

This book features a collection of up-to-date research papers that study various aspects of general operator algebra theory and concrete classes of operators, including a range of applications. Most of the papers included were presented at the International Workshop on Operator Algebras, Toeplitz Operators, and Related Topics, in Boca del Rio, Veracruz, Mexico, in November 2018. The conference, which was attended by more than 30 leading experts in the field, was held in celebration of Nikolai Vasilevski’s 70th birthday, and the contributions are dedicated to him.