Necessary and sufficient conditions for boundedness of commutators of strongly singular integral operators with weighted Lipschitz functions

被引：0
作者：
Xiaosha Zhou
Lanzhe Liu
机构：
[1] Changsha University of Science and Technology,College of Mathematics
来源：
Indian Journal of Pure and Applied Mathematics | 2011年 / 42卷
关键词：
Strongly singular integral operator; Commutator; Weighted Lipschitz space;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we prove the commutator Tb generated by the strongly singular integral operator T and the function b is bounded from Lp(w) to Lq(w1−q) if and only if b ∈ Lipβ(w), where w ∈ A1, 0 < β < 1, 1 < p < n/β and 1/q = 1/p − β/n. To do this, we first show a maximal function estimate for the commutator.
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页码：405 / 416
页数：11
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共 27 条
[11]  
Fefferman C.(1978)Mean oscillation and commutators of singular integral operators Ark. Math. 16 263-270
[12]  
Fefferman C.(1974)Weighted norm inequalities for fractional integral Trans. Amer. Math. Soc. 192 261-274
[13]  
Stein E. M.(1995)Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss Indiana Univ. Math. J. 44 1-17
[14]  
Garcia-Cuerva J.(1995)Endpoint estimate for commutators of singular integral operators J. Func. Anal. 128 163-185
[15]  
Harboure E.(1989)Vector-valued commutators and applications Indiana University Math. J. 38 959-971
[16]  
Segovia C.(1979)An Math. Z. 165 231-238
[17]  
Torrea J. L.(undefined) inequality for strongly singular integrals undefined undefined undefined-undefined
[18]  
Hu B.(undefined)undefined undefined undefined undefined-undefined
[19]  
Gu J.(undefined)undefined undefined undefined undefined-undefined
[20]  
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