A Boundedness Criterion via Atoms for Linear Operators in Hardy Spaces

被引：65
|
作者：
Yang, Dachun [1 ]
Zhou, Yuan [1 ]
机构：
[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China
来源：
CONSTRUCTIVE APPROXIMATION | 2009年 / 29卷 / 02期
基金：
美国国家科学基金会;
关键词：
Linear operator; Boundedness criterion; Hardy space; Atom; Calderon reproducing formula; Quasi-Banach space; HP-SPACES; VARIABLES;
D O I：
10.1007/s00365-008-9015-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let p is an element of (0, 1] and s >= [n(1/p - 1)], where [n(1/p - 1)] denotes the maximal integer no more than n(1/p - 1). In this paper, the authors prove that a linear operator T extends to a bounded linear operator from the Hardy space H(p)(R(n)) to some quasi-Banach space B if and only if T maps all (p, 2, s)-atoms into uniformly bounded elements of B.
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页码：207 / 218
页数：12
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