与非光滑核的奇异积分相关的Toeplitz算子的双权估计

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (6): 1122-1132.

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Two Weighted Estimates for Toeplitz Operator Related to Singular Integrals Operator with Non-smooth Kernels

CHEN Dong-Xiang, LI Qian-Li

College of Mathematics and Information, Jiangxi Normal University, Nanchang 330022

Received:2012-08-07 Revised:2013-10-24 Online:2013-12-25 Published:2013-12-25
Supported by:
国家自然科学基金(10961015, 11261023)、江西省自然科学基金(20122BAB201011)和江西省教育厅基金(GJJ10397)资助

Abstract

Abstract:

This paper is concerned with pointwise estimates for the sharp maximal function of the Toeplitz operators T_b related to singular integral operators with non-smooth kernel and a weighted Lipschitz function. We show that Toeplitz operator T_b is bounded from L^p(ω) to L^q(ω^1-q). On the other hand, we also establish pointwise estimates for the sharp maximal function of the Toeplitz operator related to singular integral operators with non-smooth kernel and a weighted BMO function and show that this Toeplitz operator T_b is bounded from L^p(μ) to L^p(ν).

Key words: Toeplitz operator, Weighted Lipschitz spaces, Weighted BMO(ω) space, Two weighted estimate

CLC Number:

42B25

CHEN Dong-Xiang, LI Qian-Li. Two Weighted Estimates for Toeplitz Operator Related to Singular Integrals Operator with Non-smooth Kernels[J].Acta mathematica scientia,Series A, 2013, 33(6): 1122-1132.

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Two Weighted Estimates for Toeplitz Operator Related to Singular Integrals Operator with Non-smooth Kernels

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