Summability of multi-dimensional fourier series and hardy spaces

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Bibliographic Information

Summability of multi-dimensional fourier series and hardy spaces

by Ferenc Weisz

(Mathematics and its applications, Vol.541)

Kluwer Academic, c2002

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Note

Includes reference (p.315-330) and index

Description and Table of Contents

Description

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].

Table of Contents

Preface. Acknowledgments. 1. Multi-Dimensional Dyadic Hardy Spaces. 2. Multi-Dimensional Classical Hardy Spaces. 3. Summability of D-Dimensional Walsh-Fourier Series. 4. The D-Dimensional Dyadic Derivative. 5. Summability of D-Dimensional Trigonometric-Fourier Series. 6. Summability of D-Dimensional Fourier Transforms. 7. Spline and Ciesielski Systems. References. Index.

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Details

  • NCID
    BA57084412
  • ISBN
    • 1402005644
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    xv, 332 p.
  • Size
    25 cm
  • Parent Bibliography ID
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