多线性分数次积分算子有界的充分必要条件

数学物理学报 ›› 2015, Vol. 35 ›› Issue (6): 1106-1114.

多线性分数次积分算子有界的充分必要条件

王松柏¹, 潘继斌¹, 江寅生²

1 湖北师范学院数学与统计学院湖北黄石 435002;
2 新疆大学数学与系统科学学院乌鲁木齐 830046

收稿日期:2015-04-16 修回日期:2015-10-11 出版日期:2015-12-25 发布日期:2015-12-25
作者简介:江寅生,ysjiang@xju.edu.cn
基金资助:
国家自然科学基金(11161044,11261055)资助

Necessary and Sufficient Conditions for Boundedness of Commutators of Multilinear Fractional Integral Operators

Wang Songbai¹, Pan Jibing¹, Jiang Yinsheng²

1 College of Mathematics and statistics, Hubei Normal University, Huangshi 435002;
2 College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046

Received:2015-04-16 Revised:2015-10-11 Online:2015-12-25 Published:2015-12-25

摘要/Abstract

摘要：

令ω∈ A₁, 0<α<mn和0<β<1满足条件α+β<mn.又设1<p₁,…,p_m<∞使得1/q=1/p-(α+β)/n>0并且1/p=1/p₁+…+1/p_m.这时我们有b∈Lip_β(ω) ×…×Lip_β(ω)当且仅当由多线性分数次算子I_α与函数向量b生成的线性交换子[Σb,I_α]是从L^p₁(ω)×…×L^p_m(ω)到L^q(ω^1-(1-α/n)q)有界的.

关键词: 多线性分数次积分, Lip_&beta, 空间, 交换子

Abstract:

Let ω∈A₁, 0<α<mn and 0<β<1 such that α+β<mn, and let 1<p₁,…,p_m<∞ with 1/q=1/p-(α+β)/n>0 and 1/p=1/p₁+…+1/p_m. We obtain that b∈Lip_β(ω)^m if and only if the commutators[Σb,I_α] generated by multilinear fractional integral operators I_α and the symbols b are bounded from L^p₁(ω)× …× L^p_m(ω) to L^q(ω^1-(1-α/n)q).

Key words: Multilinear fractional integral operator, Lip_β spaces, Commutators

中图分类号:

O174.2

王松柏, 潘继斌, 江寅生. 多线性分数次积分算子有界的充分必要条件[J]. 数学物理学报, 2015, 35(6): 1106-1114.

Wang Songbai, Pan Jibing, Jiang Yinsheng. Necessary and Sufficient Conditions for Boundedness of Commutators of Multilinear Fractional Integral Operators[J]. Acta mathematica scientia,Series A, 2015, 35(6): 1106-1114.

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