Ferenc Weisz

(Author)

Summability of Multi-Dimensional Fourier Series and Hardy Spaces (2002)Hardcover - 2002, 31 March 2002

Summability of Multi-Dimensional Fourier Series and Hardy Spaces (2002)
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Part of Series
Mathematics and Its Applications
Print Length
332 pages
Language
English
Publisher
Springer
Date Published
31 Mar 2002
ISBN-10
1402005644
ISBN-13
9781402005640

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].

Product Details

Author:
Ferenc Weisz
Book Edition:
2002
Book Format:
Hardcover
Country of Origin:
US
Date Published:
31 March 2002
Dimensions:
25.2 x 16.05 x 2.03 cm
ISBN-10:
1402005644
ISBN-13:
9781402005640
Language:
English
Location:
Dordrecht
Pages:
332
Publisher:
Weight:
757.5 gm

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