Real-Variable Theory of Musielak-Orlicz Hardy Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Real-Variable Theory of Musielak-Orlicz Hardy Spaces write by Dachun Yang. This book was released on 2017-05-09. Real-Variable Theory of Musielak-Orlicz Hardy Spaces available in PDF, EPUB and Kindle. 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.
Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko
Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko write by Yinqin Li. This book was released on 2023-02-14. Real-Variable Theory of Hardy Spaces Associated with Generalized Herz Spaces of Rafeiro and Samko available 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.
Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series
Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series write by Lars-Erik Persson. This book was released on 2022-11-22. Martingale Hardy Spaces and Summability of One-Dimensional Vilenkin-Fourier Series available in PDF, EPUB and Kindle. This book discusses, develops and applies the theory of Vilenkin-Fourier series connected to modern harmonic analysis. The classical theory of Fourier series deals with decomposition of a function into sinusoidal waves. Unlike these continuous waves the Vilenkin (Walsh) functions are rectangular waves. Such waves have already been used frequently in the theory of signal transmission, multiplexing, filtering, image enhancement, code theory, digital signal processing and pattern recognition. The development of the theory of Vilenkin-Fourier series has been strongly influenced by the classical theory of trigonometric series. Because of this it is inevitable to compare results of Vilenkin-Fourier series to those on trigonometric series. There are many similarities between these theories, but there exist differences also. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. The first part of the book can be used as an introduction to the subject, and the following chapters summarize the most recent research in this fascinating area and can be read independently. Each chapter concludes with historical remarks and open questions. The book will appeal to researchers working in Fourier and more broad harmonic analysis and will inspire them for their own and their students' research. Moreover, researchers in applied fields will appreciate it as a sourcebook far beyond the traditional mathematical domains.
Function Spaces and Inequalities
Function Spaces and Inequalities - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Function Spaces and Inequalities write by Pankaj Jain. This book was released on 2017-10-20. Function Spaces and Inequalities available in PDF, EPUB and Kindle. This book features original research and survey articles on the topics of function spaces and inequalities. It focuses on (variable/grand/small) Lebesgue spaces, Orlicz spaces, Lorentz spaces, and Morrey spaces and deals with mapping properties of operators, (weighted) inequalities, pointwise multipliers and interpolation. Moreover, it considers Sobolev–Besov and Triebel–Lizorkin type smoothness spaces. The book includes papers by leading international researchers, presented at the International Conference on Function Spaces and Inequalities, held at the South Asian University, New Delhi, India, on 11–15 December 2015, which focused on recent developments in the theory of spaces with variable exponents. It also offers further investigations concerning Sobolev-type embeddings, discrete inequalities and harmonic analysis. Each chapter is dedicated to a specific topic and written by leading experts, providing an overview of the subject and stimulating future research.
Orlicz Spaces and Generalized Orlicz Spaces
Orlicz Spaces and Generalized Orlicz Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Orlicz Spaces and Generalized Orlicz Spaces write by Petteri Harjulehto. This book was released on 2019-05-07. Orlicz Spaces and Generalized Orlicz Spaces available 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.
