The molecular characterization of weighted Hardy spaces

被引：60
|
作者：
Lee, MY [1 ]
Lin, CC [1 ]
机构：
[1] Natl Cent Univ, Dept Math, Chungli 320, Taiwan
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2002年 / 188卷 / 02期
关键词：
A(p) weights; atomic decomposition; molecular character; Hilbert transform; Riesz transforms; singular integrals; weighted Hardy spaces;
D O I：
10.1006/jfan.2001.3839
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We first define molecules for weighted Hardy spaces and prove their molecular characters. As an application, we give sufficient conditions on the kernel k such that the convolution operator Tf = k * f is bounded on weighted Hardy spaces H-w(p)(R-n), w is an element of A(1). We also get the H-w(p)(R), 1/2 < p <= 1, boundedness of the Hilbert transform and the H-w(p) (R-n), n/(n + 1) < p <= 1, boundedness of the Riesz transforms. (C) 2002 Elsevier Science (USA).
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页码：442 / 460
页数：19
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