Borderline weighted estimates for commutators of singular integrals
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<...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42872 |
| Acceso en línea: | http://hdl.handle.net/11441/42872 |
| Access Level: | acceso abierto |
| Palabra clave: | commutators Rubio de Francia extrapolation Ap weights Hardy-Littlewood maximal function |
| Sumario: | 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. |
|---|