Artículo
Borderline weighted estimates for commutators of singular integrals
Autor/es | Pérez Moreno, Carlos
Rivera Ríos, Israel Pablo |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2016 |
Fecha de depósito | 2016-06-29 |
Publicado en |
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Resumen | In 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 ... In 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. |
Agencias financiadoras | Ministerio de Economía y Competitividad (MINECO). España |
Identificador del proyecto | info:eu-repo/grantAgreement/MINECO/MTM2014-53850-P
info:eu-repo/grantAgreement/MINECO/MTM2012-30748 |
Cita | Pérez Moreno, C. y Rivera Ríos, I.P. (2016). Borderline weighted estimates for commutators of singular integrals. Israel Journal of Mathematics |
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