Summability of Multi-Dimensional Fourier Series and Hardy Spaces

  • Ferenc Weisz

Part of the Mathematics and Its Applications book series (MAIA, volume 541)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Ferenc Weisz
    Pages 1-64
  3. Ferenc Weisz
    Pages 65-109
  4. Ferenc Weisz
    Pages 155-189
  5. Ferenc Weisz
    Pages 265-314
  6. Back Matter
    Pages 315-332

About this book

Introduction

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].

Keywords

Fourier transform Martingale Maxima Probability theory Stochastic processes distribution stochastic process

Authors and affiliations

  • Ferenc Weisz
    • 1
  1. 1.Department of Numerical AnalysisEötvös Loránd UniversityBudapestHungary

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-3183-6
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-5992-5
  • Online ISBN 978-94-017-3183-6
  • About this book
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