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 2002-03-31. 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. Martingale Hardy Spaces and Summability of One-dimensional Vilenkin-Fourier Series available in PDF, EPUB and Kindle.
Hardy Martingales
Hardy Martingales - 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 Hardy Martingales write by Paul F. X. Müller. This book was released on 2022-07-14. Hardy Martingales available in PDF, EPUB and Kindle. This book presents the probabilistic methods around Hardy martingales for an audience interested in their applications to complex, harmonic, and functional analysis. Building on work of Bourgain, Garling, Jones, Maurey, Pisier, and Varopoulos, it discusses in detail those martingale spaces that reflect characteristic qualities of complex analytic functions. Its particular themes are holomorphic random variables on Wiener space, and Hardy martingales on the infinite torus product, and numerous deep applications to the geometry and classification of complex Banach spaces, e.g., the SL∞ estimates for Doob's projection operator, the embedding of L1 into L1/H1, the isomorphic classification theorem for the polydisk algebras, or the real variables characterization of Banach spaces with the analytic Radon Nikodym property. Due to the inclusion of key background material on stochastic analysis and Banach space theory, it's suitable for a wide spectrum of researchers and graduate students working in classical and functional analysis.
