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http://dx.doi.org/10.4134/BKMS.b171076

QUANTITATIVE WEIGHTED BOUNDS FOR THE VECTOR-VALUED SINGULAR INTEGRAL OPERATORS WITH NONSMOOTH KERNELS  

Hu, Guoen (School of Applied Mathematics Beijing Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1791-1809 More about this Journal
Abstract
Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q(q{\in}(1,{\infty}))$ be the vector-valued operator defined by $T_qf(x)=({\sum}_{k=1}^{\infty}{\mid}T\;f_k(x){\mid}^q)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of L log L type for the grand maximal operator of T, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.
Keywords
weighted bound; singular integral operator; nonsmooth kernel; sparse operator; sharp maximal operator;
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Times Cited By KSCI : 1  (Citation Analysis)
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