Calderon-Zygmund; 算子在乘積空間上的 H^p(R^n × R^m) 有界性 H^p(R^n × R^m) boundedness of Calderon-Zygmund operators

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/43901

Title:	Calderon-Zygmund;算子在乘積空間上的 H^p(R^n × R^m) 有界性 H^p(R^n × R^m) boundedness of Calderon-Zygmund operators
Authors:	許谷榕;KU-JUNG HSU
Contributors:	數學研究所
Keywords:	乘積空間;奇異積分算子;有界性;哈地空間;Hardy spaces;singular integral operators;product space;boundedness
Date:	2010-06-23
Issue Date:	2010-12-08 14:25:58 (UTC+8)
Publisher:	國立中央大學
Abstract:	本論文的主要目的，是去討論乘積空間上的 H^p( R^n × R^m) 有界性。在這篇論文裡，應用了 Calderon 表示定理、向量值的奇異積分、Littlewood-Paley 理論、Fefferman 的矩形原子分解和 Journe 的覆蓋引理等方法去證明 T 在 H^p(R^n × R^m),max{n/(n+ε),m/(m+ε)}<p<= 1 上有界性的充分必要條件為 T_{1}(1)=T_{2}(1)=0，其中 ε 是關於 T 的算子核的正則指數。 The main purpose of this paper is to discuss H^p(R^n × R^m) boundedness of Calderon-Zygmund operators. We apply vector-valued singular integral, Calderon's identity, Littlewood-Paley theory and the almost orthogonality together with Fefferman's rectangle atomic decomposition and Journe's covering lemma to show that T is bounded on product H^p(R^n × R^m) for max{n/(n+ε),m/(m+ε)} <p<=1 if and only if T_{1}(1)=T_{2}(1)=0, where ε is the regularity exponent of the kernel of T.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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