Marcinkiewicz integral on Hardy spaces

被引：70

作者：

Ding, Y ^{[1
]}

Lu, SZ ^{[1
]}

Xue, QY ^{[1
]}

机构：

[1] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2002年 / 42卷 / 02期

基金：

中国国家自然科学基金;

关键词：

42B25; 42B30;

D O I：

10.1007/BF01275514

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove that the Marcinkiewicz integral mu(Omega) is an operator of type (H-1, L-1) and of type (H-1,H-infinity, L-1,L-infinity). As a corollary of the results above, we obtain again the the weak type (1,1) boundedness of mu(Omega), but the smoothness condition assumed on Omega is weaker than Stein's condition.

引用

页码：174 / 182

页数：9

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]

CALDERON AP, 1967, P S PURE MATH, V10, P56

[3] MAXIMAL ESTIMATES FOR CESARO AND RIESZ MEANS ON SPHERES [J].

COLZANI, L ;

TAIBLESON, MH ;

WEISS, G .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1984, 33 (06) :873-889

[4]

Colzani L., 1982, Ph. D. Thesis

[5] Lp-boundedness of Marcinkiewicz integrals with Hardy space function kernels [J].

Ding, Y ;

Fan, DS ;

Pan, YB .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2000, 16 (04) :593-600

[6]

FEFFERMAN R, 1987, STUD MATH, V85, P1

[7]

KUTZ D, 1979, T AM MATH SOC, V255, P343

[8]

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]

[9]

STEIN EM, 1993, HARMONIC ANAL REAL V

← 1 →