Real Variable Theory Of Hardy Spaces Associated With Generalized Herz Spaces Of Rafeiro And Samko PDF Download
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Author | : Yinqin Li |
Publisher | : Springer Nature |
Total Pages | : 663 |
Release | : 2023-02-14 |
Genre | : Mathematics |
ISBN | : 9811967881 |
Download Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko Book in PDF, ePub and Kindle
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.
Author | : Christian Constanda |
Publisher | : Springer Nature |
Total Pages | : 189 |
Release | : |
Genre | : |
ISBN | : 3031595912 |
Download Exact and Approximate Solutions for Mathematical Models in Science and Engineering Book in PDF, ePub and Kindle
Author | : Gerald B. Folland |
Publisher | : Princeton University Press |
Total Pages | : 302 |
Release | : 2020-12-08 |
Genre | : Mathematics |
ISBN | : 0691222452 |
Download Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28 Book in PDF, ePub and Kindle
The object of this monograph is to give an exposition of the real-variable theory of Hardy spaces (HP spaces). This theory has attracted considerable attention in recent years because it led to a better understanding in Rn of such related topics as singular integrals, multiplier operators, maximal functions, and real-variable methods generally. Because of its fruitful development, a systematic exposition of some of the main parts of the theory is now desirable. In addition to this exposition, these notes contain a recasting of the theory in the more general setting where the underlying Rn is replaced by a homogeneous group. The justification for this wider scope comes from two sources: 1) the theory of semi-simple Lie groups and symmetric spaces, where such homogeneous groups arise naturally as "boundaries," and 2) certain classes of non-elliptic differential equations (in particular those connected with several complex variables), where the model cases occur on homogeneous groups. The example which has been most widely studied in recent years is that of the Heisenberg group.
Author | : Marcin Bownik |
Publisher | : American Mathematical Soc. |
Total Pages | : 136 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082183326X |
Download Anisotropic Hardy Spaces and Wavelets Book in PDF, ePub and Kindle
Investigates the anisotropic Hardy spaces associated with very general discrete groups of dilations. This book includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon and Torchinsky.
Author | : Vakhtang Kokilashvili |
Publisher | : Birkhäuser |
Total Pages | : 455 |
Release | : 2016-05-12 |
Genre | : Mathematics |
ISBN | : 3319210181 |
Download Integral Operators in Non-Standard Function Spaces Book in PDF, ePub and Kindle
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.
Author | : Petteri Harjulehto |
Publisher | : Springer |
Total Pages | : 169 |
Release | : 2019-05-07 |
Genre | : Mathematics |
ISBN | : 303015100X |
Download Orlicz Spaces and Generalized Orlicz Spaces Book in PDF, ePub and Kindle
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 | : Hemen Dutta |
Publisher | : CRC Press |
Total Pages | : 339 |
Release | : 2020-12-22 |
Genre | : Mathematics |
ISBN | : 1000204219 |
Download Topics in Contemporary Mathematical Analysis and Applications Book in PDF, ePub and Kindle
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.
Author | : Vakhtang Kokilashvili |
Publisher | : Birkhäuser |
Total Pages | : 585 |
Release | : 2016-05-11 |
Genre | : Mathematics |
ISBN | : 3319210157 |
Download Integral Operators in Non-Standard Function Spaces Book in PDF, ePub and Kindle
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.
Author | : Yoshihiro Sawano |
Publisher | : |
Total Pages | : 102 |
Release | : 2017 |
Genre | : |
ISBN | : |
Download Hardy Spaces for Ball Quasi-Banach Function Spaces Book in PDF, ePub and Kindle
Author | : Lars Diening |
Publisher | : Springer |
Total Pages | : 516 |
Release | : 2011-03-29 |
Genre | : Mathematics |
ISBN | : 3642183638 |
Download Lebesgue and Sobolev Spaces with Variable Exponents Book in PDF, ePub and Kindle
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.