| 書目名稱 | Summability of Multi-Dimensional Fourier Series and Hardy Spaces | | 編輯 | Ferenc Weisz | | 視頻video | http://file.papertrans.cn/882/881702/881702.mp4 | | 叢書名稱 | Mathematics and Its Applications | | 圖書封面 |  | | 描述 | 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 | | 出版日期 | Book 2002 | | 關(guān)鍵詞 | Fourier transform; Martingale; Maxima; Probability theory; Stochastic processes; distribution; stochastic | | 版次 | 1 | | doi | https://doi.org/10.1007/978-94-017-3183-6 | | isbn_softcover | 978-90-481-5992-5 | | isbn_ebook | 978-94-017-3183-6 | | copyright | Springer Science+Business Media B.V. 2002 |
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