Artículo
Optimal exponents in weighted estimates without examples
Autor/es | Luque Martínez, Teresa
Pérez Moreno, Carlos Rela, Ezequiel |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2015 |
Fecha de depósito | 2016-06-29 |
Publicado en |
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Resumen | t. We present a general approach for proving the optimality
of the exponents on weighted estimates. We show that if an operator T
satisfies a bound like
kT kLp(w) ≤ c [w]
β
Ap
w ∈ Ap,
then the optimal lower bound ... t. We present a general approach for proving the optimality of the exponents on weighted estimates. We show that if an operator T satisfies a bound like kT kLp(w) ≤ c [w] β Ap w ∈ Ap, then the optimal lower bound for β is closely related to the asymptotic behaviour of the unweighted L p norm kT kLp(Rn) as p goes to 1 and +∞, which is related to Yano’s classical extrapolation theorem. By combining these results with the known weighted inequalities, we derive the sharpness of the exponents, without building any specific example, for a wide class of operators including maximal-type, Calder´on–Zygmund and fractional operators. In particular, we obtain a lower bound for the best possible exponent for Bochner-Riesz multipliers. We also present a new result concerning a continuum family of maximal operators on the scale of logarithmic Orlicz functions. Further, our method allows to consider in a unified way maximal operators defined over very general Muckenhoupt bases. |
Agencias financiadoras | Ministerio de Ciencia e Innovación (MICIN). España Junta de Andalucía |
Identificador del proyecto | MTM2012-30748
FQM-4745 |
Cita | Pérez Moreno, C. y Rela, E. (2015). Optimal exponents in weighted estimates without examples. Mathematical Research Letters, 22 (1), 183-201. |
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