WEIGHTED Lp BOUNDEDNESS OF CARLESON TYPE MAXIMAL OPERATORS

被引：6

作者：

Ding, Yong ^{[1
]}

Liu, Honghai ^{[2
]}

机构：

[1] Beijing Normal Univ, Minist Educ China, Sch Math Sci, Lab Math & Complex Syst BNU, Beijing 100875, Peoples R China

[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454000, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 140卷 / 08期

关键词：

Carleson operator; homogeneous kernel; L-q-Dini condition; A(p) weight; NORM INEQUALITIES; INTEGRALS;

D O I：

10.1090/S0002-9939-2011-11110-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In 2001, E. M. Stein and S. Wainger gave the L-p boundedness of the Carleson type maximal operator T*, which is defined by T* f(x) = sup(lambda) vertical bar integral(Rn) e(iP lambda(y)) K(y)f(x - y)dy vertical bar. In this paper, the authors show that if K is a homogeneous kernel, i.e. K(y) = Omega(y')vertical bar y vertical bar(-n), then Stein-Wainger's result still holds on the weighted L-p spaces when Omega satisfies only an L-p-Dini condition for some 1 < q <= infinity.

引用

页码：2739 / 2751

页数：13

共 14 条

[1]

Calderon A. P., 1967, P S PURE MATH, P56

[2]

Carleson L., 1966, ACTA MATH, V111, P361

[3]

Colzani L., 1982, PhD Thesis

[4] LP BOUNDEDNESS OF CARLESON TYPE MAXIMAL OPERATORS WITH NONSMOOTH KERNELS [J].

Ding, Yong ;

Liu, Honghai .

TOHOKU MATHEMATICAL JOURNAL, 2011, 63 (02) :255-267

[5] WEIGHTED NORM INEQUALITIES FOR HOMOGENEOUS SINGULAR-INTEGRALS [J].

DUOANDIKOETXEA, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 336 (02) :869-880

[6]

Garcfa-Cuerva J., 1985, MATH STUDIES, V116

[7]

Hunt R. A., 1967, P C HELD SO ILL U ED

[8] WEIGHTED NORM INEQUALITY FOR FOURIER-SERIES [J].

HUNT, RA ;

YOUNG, WS .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 80 (02) :274-277

[9] RESULTS ON WEIGHTED NORM INEQUALITIES FOR MULTIPLIERS [J].

KURTZ, DS ;

WHEEDEN, RL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 255 (NOV) :343-362

[10] A Littlewood-Paley inequality for the Carleson operator [J].

Prestini, E ;

Sjölin, P .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2000, 6 (05) :457-466

← 1 2 →