Extrapolation and sharp norm estimates for classical operators on weighted Lebesgue spaces

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Fecha:	2005
Resumen:	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.
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Lengua:	Anglès
Documento:	Article ; recerca ; Versió publicada
Materia:	Extrapolation ; Sharp weighted estimates ; Dyadic square function ; Dyadic paraproduct ; Martingale transform ; Hilbert transform ; Beurling transform
Publicado en:	Publicacions matemàtiques, V. 49 N. 1 (2005) , p. 73-91, ISSN 2014-4350

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