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向量值奇异积分算子的核决定着算子的性质和加权不等式,标准核向量值奇异积分算子的研究内容已经日趋完善,弱Dini型核以及粗糙核向量值奇异积分算子也有所研究,但研究内容不够完善,现继续研究粗糙核向量值奇异积分算子,得到了这类算子的几个加权赋范不等式,丰富了向量值奇异积分算子的理论.
Abstract：The nature of vector-valued singular integral operators and weighted inequalities are dependent on its kernel.The research results of standard kernel vector-valued singular integral operators are nearly perfect.Weak Dini-type kernel and rough kernel vector-valued singular integral operators are studied.But the research contents are not perfect.This paper continues the study of rough kernel vector-valued singular integral operators,and it obtains the weighted inequalities of this kind of operators.So it enriches the theory of vector-valued singular integral operators.
[1]Carlos P伢rez,Rodrigo Trujillo-gonz仳lez.Sharp Weighted Estimates for Vector-valued Singular Integral Operators and Commutators[J].Tohoku Math J,2003,55(1):109-129.
[2]冯文莉,白云芬,孙庆利.Dini型核向量值奇异积分算子交换子的加权赋范不等式[J].西南师范大学学报,2010,(35)5:45-49.
[3]冯文莉,唐加冕,刘学军,等.粗糙核向量值奇异积分算子的加权不等式[J].石家庄学院学报,2012,(14)6:30-33.
[4]Carlos P伢rez.Weighted Norm Inequalities for Singular Integral Operators[J].J London Math Soc,1994,2:296-308.
基本信息:
DOI：10.13573/j.cnki.sjzxyxb.2013.03.001
中图分类号:O177.6
引用信息:
[1]冯文莉,商美娟,刘晓娣.粗糙核向量值奇异积分算子的几个加权赋范不等式[J].石家庄学院学报,2013,15(03):42-44.DOI:10.13573/j.cnki.sjzxyxb.2013.03.001.
基金信息:
河北省教育厅自然科学基金(Z2012003);; 石家庄学院自然科学基金(11YB009)
2013-04-26
2013-04-26
2013-04-26