Summability of Multi-Dimensional Fourier Series and Hardy Spaces

Ferenc Weisz (Autor)

Buch | Hardcover

332 Seiten

2002
Kluwer Academic Publishers (Verlag)
978-1-4020-0564-0 (ISBN)

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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].

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.

Erscheint lt. Verlag	31.3.2002
Reihe/Serie	Mathematics and Its Applications ; 541
Reihe/Serie	Mathematics and Its Applications ; 541
Zusatzinfo	XV, 332 p.
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4020-0564-4 / 1402005644
ISBN-13	978-1-4020-0564-0 / 9781402005640
Zustand	Neuware