Read e-book online Summability of Multi-Dimensional Fourier Series and Hardy PDF

By Ferenc Weisz

ISBN-10: 1402005644

ISBN-13: 9781402005640

The heritage of martingale concept is going again to the early fifties while Doob [57] mentioned the relationship among martingales and analytic services. at the foundation of Burkholder's clinical achievements the mar­ tingale conception can completely good be utilized in advanced research and within the idea of classical Hardy areas. This connection is the most element of Durrett's e-book [60]. The martingale thought can be good utilized in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy areas are mentioned exhaustively within the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], lengthy [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). the idea of more-parameter martingales and martingale Hardy areas is investigated in Imkeller [107] and Weisz [216]. this is often the 1st mono­ graph which considers the idea of more-parameter classical Hardy areas. The equipment of proofs for one and a number of other parameters are en­ tirely assorted; mostly the theorems said for numerous parameters are even more tricky to make sure. The so-called atomic decomposition technique that may be utilized either within the one-and more-parameter circumstances, was once thought of for martingales by means of the writer in [216].

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Summability of Multi-Dimensional Fourier Series and Hardy Spaces (Mathematics and Its Applications) by Ferenc Weisz


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