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- W1617207725 abstract "In this paper we establish the following estimate [ wleft(left{ xinmathbb{R}^{n},:,left|[b,T]f(x)right| > lambdaright} right)leq frac{c_{T}}{varepsilon^{2}}int_{mathbb{R}^{n}}Phileft(|b|_{BMO}frac{|f(x)|}{lambda}right)M_{L(log L)^{1+varepsilon}}w(x)dx ] where $wgeq0, , 0<varepsilon<1$ and $Phi(t)=t(t+log^+(t))$. This inequality relies upon the following sharp $L^p$ estimate [ |[b,T]f|_{L^{p}(w)}leq c_{T}left(p'right)^{2}p^{2}left(frac{p-1}{delta}right)^{frac{1}{p'}} |b|_{BMO} , |f |_{L^{p}(M_{L(log L)^{2p-1+delta}}w)} ]where $1<p<infty, wgeq0 text{ and } 0<delta<1.$ As a consequence we recover the following estimate [wleft({xinmathbb{R}^{n},:,left|[b,T]f(x)right| >lambda}right)leq c_T,[w]_{A_{infty}}left(1+log^{+}[w]_{A_{infty}}right)^{2}int_{mathbb{R}^{n}} Phileft(|b|_{BMO}frac{|f(x)|}{lambda}right)Mw(x)dx] We also obtain the analogue estimates for symbol-multilinear commutators for a wider class of symbols." @default.
- W1617207725 created "2016-06-24" @default.
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- W1617207725 date "2017-03-01" @default.
- W1617207725 modified "2023-09-30" @default.
- W1617207725 title "Borderline weighted estimates for commutators of singular integrals" @default.
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- W1617207725 doi "https://doi.org/10.1007/s11856-017-1454-6" @default.
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