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In this paper, we investigate the weighted vector-valued \linebreak bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\,\mathbb{R}^n,w_1)\times\dots\times L^{p_m}(l^{q_m};\,\mathbb{R}^n,w_m)$ to $L^{p}(l^q;\mathbb{R}^n$, $\nu_{\vec{w}})$, with $p_1,\ldots,p_m$, $q_1,\ldots,q_m\in (1,\,\infty)$, $1/p=1/p_1+\dots+1/p_m$, $1/q=1/q_1+\dots+1/q_m$ and $\vec{w}=(w_1,\ldots,w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the Calder\'on commutator.
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참고문헌 (36)
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
A. Bui / Weighted bounds for multilinear operators with non-smooth kernels / arxiv:1506.07752
A.-P. Calderon / 1965 / Commutators of singular integral operators / Proc. Nat. Acad. Sci. U.S.A. 53:1092~1099
C. P. Calderon / 1975 / On commutators of singular integrals / Studia Math. 53(2):139~174
D. Chung / 2012 / Sharp bounds for general commutators on weighted Lebesgue spaces / Trans. Amer. Math. Soc. 364(3):1163~1177
A. Bui / Weighted bounds for multilinear operators with non-smooth kernels / arxiv:1506.07752
A.-P. Calderon / 1965 / Commutators of singular integral operators / Proc. Nat. Acad. Sci. U.S.A. 53:1092~1099
C. P. Calderon / 1975 / On commutators of singular integrals / Studia Math. 53(2):139~174
D. Chung / 2012 / Sharp bounds for general commutators on weighted Lebesgue spaces / Trans. Amer. Math. Soc. 364(3):1163~1177
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