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

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