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Summability of Multi-Dimensional Fourier Series and Hardy Spaces

  • Book
  • © 2002

Overview

Authors:
  1. Ferenc Weisz

    1. Department of Numerical Analysis, Eötvös Loránd University, Budapest, Hungary

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xv
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  2. Multi-Dimensional Dyadic Hardy Spaces

    • Ferenc Weisz
    Pages 1-64

  3. Multi-Dimensional Classical Hardy Spaces

    • Ferenc Weisz
    Pages 65-109

  4. Summability of D-Dimensional Walsh-Fourier Series

    • Ferenc Weisz
    Pages 111-153

  5. The D-Dimensional Dyadic Derivative

    • Ferenc Weisz
    Pages 155-189

  6. Summability of D-Dimensional Trigonometric-Fourier Series

    • Ferenc Weisz
    Pages 191-245

  7. Summability of D-Dimensional Fourier Transforms

    • Ferenc Weisz
    Pages 247-263

  8. Spline and Ciesielski Systems

    • Ferenc Weisz
    Pages 265-314

  9. Back Matter

    Pages 315-332
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Keywords

About this book

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].

Authors and Affiliations

  • Department of Numerical Analysis, Eötvös Loránd University, Budapest, Hungary

    Ferenc Weisz

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