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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.
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참고문헌 (19)
참고문헌 신청
S. M. Buckley / 1993 / Estimates for operator norms on weighted spaces and reverse Jensen inequalities / Trans. Amer. Math. Soc 340(1):253~272
M. Carozza / 1996 / Di Napoli, Composition of maximal operators / Publ. Mat 40(2):397~409
Jiecheng Chen / 2018 / Weighted vector-valued bounds for a class of multilinear singular integral operators and applications / 대한수학회지 55(3):671~694
D. Cruz-Uribe / 2012 / Sharp weighted estimates for classical operators / Adv. Math 229(1):408~441
O. Dragicevic / 2005 / Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces / Publ. Mat 49(1):73~91
M. Carozza / 1996 / Di Napoli, Composition of maximal operators / Publ. Mat 40(2):397~409
Jiecheng Chen / 2018 / Weighted vector-valued bounds for a class of multilinear singular integral operators and applications / 대한수학회지 55(3):671~694
D. Cruz-Uribe / 2012 / Sharp weighted estimates for classical operators / Adv. Math 229(1):408~441
O. Dragicevic / 2005 / Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces / Publ. Mat 49(1):73~91
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