Remarks on Littlewood-Paley functions and singular integrals

被引：15

作者：

Fan, D ^{[1
]}

Sato, S

机构：

[1] Univ Wisconsin, Dept Math, Milwaukee, WI 53201 USA

[2] Kanazawa Univ, Fac Educ, Dept Math, Kanazawa, Ishikawa 9201192, Japan

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2002年 / 54卷 / 03期

关键词：

Littlewood-Paley functions; singular integrals;

D O I：

10.2969/jmsj/1191593909

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the generalized Littlewood-Paley square functions arising from rough kernels and prove the L-p-boundedness for a certain range of p depending on the kernel. We also study a class of singular integrals by similar methods.

引用

页码：565 / 585

页数：21

共 21 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] 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

[3]

Ding Y, 1999, INDIANA U MATH J, V48, P1037

[4]

Ding Y, 2000, HOKKAIDO MATH J, V29, P537

[5]

DING Y, PROBLEM ROUGH PARAME

[6]

DING Y, LP BOUNDEDNESS MARCI

[7] MAXIMAL AND SINGULAR INTEGRAL-OPERATORS VIA FOURIER-TRANSFORM ESTIMATES [J].

DUOANDIKOETXEA, J ;

DEFRANCIA, JLR .

INVENTIONES MATHEMATICAE, 1986, 84 (03) :541-561

[8]

FAN D, 2001, IN PRESS TOHOKU MATH, V53

[9] A singular integral operator with rough kernel [J].

Fan, DS ;

Pan, YB .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (12) :3695-3703

[10] INEQUALITIES FOR STRONGLY SINGULAR CONVOLUTION OPERATORS [J].

FEFFERMAN, C .

ACTA MATHEMATICA UPPSALA, 1970, 124 (1-2) :9-+

← 1 2 3 →