Martingale Hardy Spaces and their Applications in Fourier Analysis - 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 their Applications in Fourier Analysis write by Ferenc Weisz. This book was released on 2006-11-15. Martingale Hardy Spaces and their Applications in Fourier Analysis available in PDF, EPUB and Kindle. This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.
Variable Martingale Hardy Spaces and Their Applications in Fourier Analysis
Variable Martingale Hardy Spaces and Their Applications in Fourier Analysis - 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 Variable Martingale Hardy Spaces and Their Applications in Fourier Analysis write by Yong Jiao. This book was released on 2020. Variable Martingale Hardy Spaces and Their Applications in Fourier Analysis available in PDF, EPUB and Kindle. Key words and phrases: variable exponent, martingale Hardy space, atomic decomposition, martingale inequality, Walsh-Fourier series, Fejér means, maximal Fejér operator.
Summability of Multi-Dimensional Fourier Series and Hardy Spaces
Summability of Multi-Dimensional Fourier Series and 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 Summability of Multi-Dimensional Fourier Series and Hardy Spaces write by Ferenc Weisz. This book was released on 2013-06-29. Summability of Multi-Dimensional Fourier Series and Hardy Spaces available in PDF, EPUB and Kindle. The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216].
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.
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.
