Calderon-Zygmund; 算子的研究(I) On the Calderon-Zygmund Operators(I)

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/43094

Title:	Calderon-Zygmund;算子的研究(I) On the Calderon-Zygmund Operators(I)
Authors:	林欽誠
Contributors:	數學系
Keywords:	數學類
Date:	2006-07-01
Issue Date:	2010-12-06 16:20:11 (UTC+8)
Publisher:	行政院國家科學委員會
Abstract:	在本計畫中，我們探討非捲積型Calderon-Zygmund奇異積分算子的若干問題，包括L p、H p、BMO空間上的有界性及加權有界性，及T1定理、Tb定理。我們也考慮Calderon-Zygmund奇異積分算子所形成的集合是否會成為一個代數(Algebra)？因為垂直正交的小波基底針對Tb定理中，b是accretive函數時，Calderon-Zygmund奇異積分算子所形成的集合是一個代數。然而，當我們考慮b是更一般的para-accretive函數時，小波基底就已經不再適用；我們只能改用Calderon表示定理來處理。此外，我們也探討Calderon-Zygmund算子在乘積空間上的有界性之估計。 In this proposal we consider some problems of non-convolution type Calderon-Zygmund singular integral operators, including (weighted) L p, H p, BMO boundedness, and T1 theorem, Tb theorem. We also consider the algebra of Calderon-Zygmund operators associated to para-accretive functions. It is known that, by use of the orthonormal wavelet basis associated to accretive functions, all Calderon-Zygmund operators satisfying certain conditions form an algebra. However, the orthonormal wavelet basis is not available for the general para-accretive functions. One possibility to fix the problem is to apply the discrete Calderon-type reproducing formula associated to para-accretive functions. Moreover, we also consider the boundedness of Calderon-Zygmund operators on the product dormain. 研究期間：9408 ~ 9507
Relation:	財團法人國家實驗研究院科技政策研究與資訊中心
Appears in Collections:	[Department of Mathematics] Research Project

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