Web of Science: 83 cites, Scopus: 78 cites, Google Scholar: cites
Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces
Dragicevic, Oliver
Grafakos, Loukas
Pereyra, María Cristina
Petermichl, Stefanie

Data: 2005
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; Versió publicada
Matèria: Extrapolation ; Sharp weighted estimates ; Dyadic square function ; Dyadic paraproduct ; Martingale transform ; Hilbert transform ; Beurling transform
Publicat a: Publicacions matemàtiques, V. 49 N. 1 (2005) , p. 73-91, ISSN 2014-4350

Adreça alternativa: https://www.raco.cat/index.php/PublicacionsMatematiques/article/view/128392
DOI: 10.5565/PUBLMAT_49105_03


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