Marcinkiewicz integral on weighted Hardy spaces

被引：17
作者：
Ding, Y [1 ]
Lee, MY
Lin, CC
机构：
[1] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China
[2] Natl Cent Univ, Dept Math, Chungli 32054, Taiwan
来源：
ARCHIV DER MATHEMATIK | 2003年 / 80卷 / 06期
基金：
中国国家自然科学基金;
关键词：
D O I：
10.1007/s00013-003-4660-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we give sufficient conditions to imply the H-omega(1)-L-omega(1) boundedness of the Marcinkiewicz integral operator mu(Omega), where omega is a Muckenhoupt weight. We also prove that, under the stronger condition Omega is an element of Lip(alpha) the operator mu(Omega) is bounded from H-omega(p) to L-omega(p) for max{n/(n+ 1/2), n/(n + alpha)} < p < 1.
引用
收藏
页码：620 / 629
页数：10
相关论文
共 9 条
[1]   CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS [J].
BENEDEK, A ;
PANZONE, R ;
CALDERON, AP .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1962, 48 (03) :356-&
[2]  
DeFrancia J.L.R., 1985, WEIGHTED NORM INEQUA
[3]   Homogeneous fractional integrals on Hardy spaces [J].
Ding, Y ;
Lu, SZ .
TOHOKU MATHEMATICAL JOURNAL, 2000, 52 (01) :153-162
[4]  
Ding Y, 1999, INDIANA U MATH J, V48, P1037
[5]  
Garc?a-Cuerva J., 1979, DISS MATH, V162, P63
[6]   RESULTS ON WEIGHTED NORM INEQUALITIES FOR MULTIPLIERS [J].
KURTZ, DS ;
WHEEDEN, RL .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 255 (NOV) :343-362
[7]  
Stein E., 1958, T. Am. Math. Soc., V88, P430, DOI [DOI 10.1090/S0002-9947-1958-0112932-2, 10.1090/S0002-9947-1958-0112932-2]
[8]  
STROMBERG JO, 1985, T AM MATH SOC, V287, P293
[9]  
Torchinsky A, 1990, Colloq.Math., V60, P235
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