Artículo
Optimal exponents in weighted estimates without examples
Fecha de publicación:
13/04/2015
Editorial:
International Press Boston
Revista:
Mathematical Research Letters
ISSN:
1073-2780
e-ISSN:
1945-001X
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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 ∥ T ∥ Lp(w) ≤ c [w]βAp w ε Ap, then the optimal lower bound for β is closely related to the asymptotic behaviour of the unweighted Lp norm ∥ T ∥ Lp(Rn) as p goes to 1 and +∞. 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 maximaltype, Caldeŕon-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.
Palabras clave:
Muckenhoupt weights
,
Calderon-Zygmund operators
,
Maximal functions
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Citación
Luque, Teresa Guadalupe; Pérez Moreno, Carlos; Rela, Ezequiel; Optimal exponents in weighted estimates without examples; International Press Boston; Mathematical Research Letters; 22; 1; 13-4-2015; 183-201
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