Título inglés |
Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces. |
Título español |
Extrapolación y estimaciones de la norma precisas para operadores clásicos en espacios de Lebesgue ponderados. |
Autor/es |
Dragicevic, Oliver ; Grafakos, Loukas ; Pereyra, María Cristina ; Petermichl, Stefanie |
Organización |
Scuola Normale Superiore, Pisa, Italia;Dep. Math. Univ. Missouri, Columbia MO, Estados Unidos;Dep. Math. Statisitics Univ. New Mexico, Albuquerque NM, Estados Unidos;Dep Math. Brown Univ., Providence, Estados Unidos |
Revista |
0214-1493 |
Publicación |
2005, 49(1): 73-91, 26 Ref. |
Tipo de documento |
articulo |
Idioma |
Inglés |
Resumen inglés |
We obtain sharp weighted Lp estimates in the Rubio de Francia extrapolation theorem in terms of the Ap characteristic constant of the weight. Precisely, if for a given 1 < r < infinity the norm of a sublinear operator on Lr(w)$ is bounded by a function of the Ar characteristic constant of the weight w, then for p > r it is bounded on Lp(v) by the same increasing function of the Ap characteristic constant of v, and for p < r it is bounded on Lp(v) by the same increasing function of the (r-1)/(p-1) power of the Ap characteristic constant of v. For some operators these bounds are sharp, but not always. In particular, we show that they are sharp for the Hilbert, Beurling, and martingale transforms. |
Clasificación UNESCO |
120213 |
Palabras clave español |
Operadores integrales ; Integrales singulares ; Acotación ; Extrapolación ; Espacios de Lebesgue |
Acceso al artículo completo |