在线阅读 --自然科学版 2014年4期《多线性位势型算子的双权弱型不等式》
多线性位势型算子的双权弱型不等式--[在线阅读]
薛丽梅1, 王会敏2, 李刚3
1. 石家庄经济学院 数理学院, 河北 石家庄 050031;
2. 河北内丘中学, 河北 内丘 054200;
3. 河北广播电视大学 开放教育学院, 河北 石家庄 050071
起止页码: 337--340页
DOI: 10.11826/j.issn.1000-5854.2014.04.004
摘要
KRn上的非负局部可积函数,且满足某弱增长条件,ARn上的函数,且其所有的一阶偏导数都属于PBMORn).给出了由KA定义的多线性位势型积分算子TAK的双权弱型(pq)不等式.

Two Weights Weak Inequalities for the Multilinear Potential Type Operators
XUE Limei1, WANG Huimin2, LI Gang3
1. School of Mathematics and Sciences, Shijiazhuang University of Economics, Hebei Shijiazhuang 050031, China;
2. Neiqiu Middle School, Hebei Neiqiu 054200, China;
3. College of Open Educaion, Hebei Radio and TV University, Hebei Shijiazhuang 050071, China
Abstract:
Let K be a non-negative and locally integrable function on Rn,which satisfies a weak growth condition.Let A be a function defined on Rn,whose all derivatives of order one belong to the space PBMO.In this paper,we get a two weights weak inequality for the multilinear potential type operators TKA.

收稿日期: 2013-9-18
基金项目: 河北省博士后科研项目择优资助(2013);河北省教育厅青年基金(QN20131071,QN20131005)

参考文献:
[1]PEREZ C.Two Weighted Inequalities for Potential and Fractional Type Maximal Operators[J].Indiana Univ Math J,1994,43:663-683.
[2]COHEN J.A Sharp Estimate for Multilinear Singular Integral on Rn[J].Indiana Univ Math J,1981,30:693-702.
[3]LI W M.Two-weight Norm Inequalities for Multilinear Potential Type Integral Operators[J].Math Nachr,2008,281:839-846.
[4]LI W M,QI J Y,ZHANG Y.Two-weight Weak-type Inequalities for Potential Type Operators[J].Appl Mathe(Series B),2008,23(3):313-318.
[5]PEREZ C.On Sufficient Conditions for the Boundedness of the Hardy-Littlewood Maximal Operator Between Weighted Lp-spaces with Different Weights[J].Proc London Math Soc,1995,71:135-157.
[6]CRUZ-URIBE D,PEREZ C.Two-weight,Weak-type Norm Inequalities for Fractional Integral,Calderon-Zygmund Operators and Commutators[J].Indiana Univ Math J,2000,49:697-721.