Quantitative weighted bounds for the vector-valued singular integral operators with nonsmooth kernels
Bull. Korean Math. Soc. 2018 Vol. 55, No. 6, 1791-1809
Published online June 29, 2018
Printed November 30, 2018
Guoen Hu
Beijing Normal University
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 $T_qf(x)=\big(\sum_{k=1}^{\infty}|Tf_k(x)|^q\big)^{1/q}$. 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
MSC numbers : 42B20
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