Artículo
Sharp bounds for general commutators on weighted Lebesgue spaces
Autor/es | Chung, Daewon
Pereyra, María Cristina Pérez Moreno, Carlos |
Departamento | Universidad de Sevilla. Departamento de Análisis Matemático |
Fecha de publicación | 2012 |
Fecha de depósito | 2016-06-16 |
Publicado en |
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Resumen | We show that if a linear operator T is bounded on weighted Lebesgue space L2(w) and obeys a linear bound with respect to the A2 constant of the weight, then its commutator [b, T ] with a function b in BMO will obey a ... We show that if a linear operator T is bounded on weighted Lebesgue space L2(w) and obeys a linear bound with respect to the A2 constant of the weight, then its commutator [b, T ] with a function b in BMO will obey a quadratic bound with respect to the A2 constant of the weight. We also prove that the kth-order commutator T k b = [b, T k−1 b ] will obey a bound that is a power (k + 1) of the A2 constant of the weight. Sharp extrapolation provides corresponding Lp(w) estimates. In particular these estimates hold for T any Calder´on-Zygmund singular integral operator. The results are sharp in terms of the growth of the operator norm with respect to the Ap constant of the weight for all 1 < p < ∞, all k, and all dimensions, as examples involving the Riesz transforms, power functions and power weights show. |
Agencias financiadoras | Ministerio de Ciencia e Innovación (MICIN). España |
Identificador del proyecto | MTM2009-08934 |
Cita | Chung, D., Pereyra, M.C. y Pérez Moreno, C. (2012). Sharp bounds for general commutators on weighted Lebesgue spaces. Transactions of the American Mathematical Society, 364 (3), 1163-1177. |
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