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＜電子ブック＞
Summability of Multi-Dimensional Fourier Series and Hardy Spaces / by Ferenc Weisz
(Mathematics and Its Applications ; 541)

版	1st ed. 2002.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2002
本文言語	英語
大きさ	XV, 332 p : online resource
著者標目	*Weisz, Ferenc author SpringerLink (Online service)
件　名	LCSH:Fourier analysis LCSH:Approximation theory LCSH:Sequences (Mathematics) LCSH:Probabilities LCSH:Functions of complex variables FREE:Fourier Analysis FREE:Approximations and Expansions FREE:Sequences, Series, Summability FREE:Probability Theory FREE:Several Complex Variables and Analytic Spaces
一般注記	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 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] HTTP:URL=https://doi.org/10.1007/978-94-017-3183-6

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