Real Variable Theory Of Hardy Spaces Associated With Generalized Herz Spaces Of Rafeiro And Samko
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Real Variable Theory Of Hardy Spaces Associated With Generalized Herz Spaces Of Rafeiro And Samko
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Author : Yinqin Li
language : en
Publisher: Springer Nature
Release Date : 2023-02-14
Real Variable Theory Of Hardy Spaces Associated With Generalized Herz Spaces Of Rafeiro And Samko written by Yinqin Li and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-14 with Mathematics categories.
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.
Exact And Approximate Solutions For Mathematical Models In Science And Engineering
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Author : Christian Constanda
language : en
Publisher: Springer Nature
Release Date : 2024-07-13
Exact And Approximate Solutions For Mathematical Models In Science And Engineering written by Christian Constanda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-13 with Mathematics categories.
This contributed volume collects papers presented during a special session on integral methods in science and engineering at the 2023 International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE), held in Cadiz, Spain from July 3-8, 2023. Covering the applications of integral methods to scientific developments in a variety of fields, the chapters in this volume are written by well-known researchers in their respective disciplines and present new results in both pure and applied mathematics. Each chapter shares a common methodology based on a combination of analytic and computational tools, an approach that makes this collection a valuable, multidisciplinary reference on how mathematics can be applied to various real-world processes and phenomena.
Integral Operators In Non Standard Function Spaces
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Author : Vakhtang Kokilashvili
language : en
Publisher: Birkhäuser
Release Date : 2016-05-12
Integral Operators In Non Standard Function Spaces written by Vakhtang Kokilashvili and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-12 with Mathematics categories.
This book, the result of the authors’ long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book’s most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Orlicz Spaces And Generalized Orlicz Spaces
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Author : Petteri Harjulehto
language : en
Publisher: Springer
Release Date : 2019-05-07
Orlicz Spaces And Generalized Orlicz Spaces written by Petteri Harjulehto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.
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.
Topics In Contemporary Mathematical Analysis And Applications
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Author : Hemen Dutta
language : en
Publisher: CRC Press
Release Date : 2020-12-22
Topics In Contemporary Mathematical Analysis And Applications written by Hemen Dutta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-22 with Mathematics categories.
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.
Theory Of Besov Spaces
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Author : Yoshihiro Sawano
language : en
Publisher: Springer
Release Date : 2018-11-04
Theory Of Besov Spaces written by Yoshihiro Sawano and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-04 with Mathematics categories.
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.
Descriptive Topology In Selected Topics Of Functional Analysis
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Author : Jerzy Kąkol
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-30
Descriptive Topology In Selected Topics Of Functional Analysis written by Jerzy Kąkol and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-30 with Mathematics categories.
"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.
Partial Differential Equations With Variable Exponents
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Author : Vicentiu D. Radulescu
language : en
Publisher: CRC Press
Release Date : 2015-06-24
Partial Differential Equations With Variable Exponents written by Vicentiu D. Radulescu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Mathematics categories.
Partial Differential Equations with Variable Exponents: Variational Methods and Qualitative Analysis provides researchers and graduate students with a thorough introduction to the theory of nonlinear partial differential equations (PDEs) with a variable exponent, particularly those of elliptic type. The book presents the most important variational
An Introductory Course In Lebesgue Spaces
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Author : Rene Erlin Castillo
language : en
Publisher: Springer
Release Date : 2016-06-23
An Introductory Course In Lebesgue Spaces written by Rene Erlin Castillo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-23 with Mathematics categories.
This book is devoted exclusively to Lebesgue spaces and their direct derived spaces. Unique in its sole dedication, this book explores Lebesgue spaces, distribution functions and nonincreasing rearrangement. Moreover, it also deals with weak, Lorentz and the more recent variable exponent and grand Lebesgue spaces with considerable detail to the proofs. The book also touches on basic harmonic analysis in the aforementioned spaces. An appendix is given at the end of the book giving it a self-contained character. This work is ideal for teachers, graduate students and researchers.
Electrorheological Fluids Modeling And Mathematical Theory
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Author : Michael Ruzicka
language : en
Publisher: Springer
Release Date : 2007-05-06
Electrorheological Fluids Modeling And Mathematical Theory written by Michael Ruzicka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Technology & Engineering categories.
This is the first book to present a model, based on rational mechanics of electrorheological fluids, that takes into account the complex interactions between the electromagnetic fields and the moving liquid. Several constitutive relations for the Cauchy stress tensor are discussed. The main part of the book is devoted to a mathematical investigation of a model possessing shear-dependent viscosities, proving the existence and uniqueness of weak and strong solutions for the steady and the unsteady case. The PDS systems investigated possess so-called non-standard growth conditions. Existence results for elliptic systems with non-standard growth conditions and with a nontrivial nonlinear r.h.s. and the first ever results for parabolic systems with a non-standard growth conditions are given for the first time. Written for advanced graduate students, as well as for researchers in the field, the discussion of both the modeling and the mathematics is self-contained.