Pérez Moreno, CarlosRivera Ríos, Israel Pablo2016-06-292016-06-292016Pérez Moreno, C. y Rivera Ríos, I.P. (2016). Borderline weighted estimates for commutators of singular integrals. Israel Journal of Mathematics0021-21721565-8511http://hdl.handle.net/11441/42872In this paper we establish the following estimate w({x∈Rn:|[b,T]f(x)|>λ})≤cTε2∫RnΦ(∥b∥BMO|f(x)|λ)ML(logL)1+εw(x)dx where w≥0,0<ε<1 and Φ(t)=t(t+log+(t)). This inequality relies upon the following sharp Lp estimate ∥[b,T]f∥Lp(w)≤cT(p′)2p2(p−1δ)1p′∥b∥BMO∥f∥Lp(ML(logL)2p−1+δw) where 1<p<∞,w≥0 and 0<δ<1. As a consequence we recover the following estimate w({x∈Rn:|[b,T]f(x)|>λ})≤cT[w]A∞(1+log+[w]A∞)2∫RnΦ(∥b∥BMO|f(x)|λ)Mw(x)dx We also obtain the analogue estimates for symbol-multilinear commutators for a wider class of symbols.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/commutatorsRubio de Francia extrapolationAp weightsHardy-Littlewood maximal functioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess