Article
Sharp weighted inequalities for the vector-valued maximal function
Author/s | Pérez Moreno, Carlos |
Department | Universidad de Sevilla. Departamento de Análisis Matemático |
Publication Date | 2000 |
Deposit Date | 2016-11-14 |
Published in |
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Abstract | We prove in this paper some sharp weighted inequalities for the
vector-valued maximal function Mq of Fefferman and Stein defined by
Mqf(x) = X∞ i=1 (M fi(x))q !1/q, where M is the Hardy-Littlewood maximal function. As a ... We prove in this paper some sharp weighted inequalities for the vector-valued maximal function Mq of Fefferman and Stein defined by Mqf(x) = X∞ i=1 (M fi(x))q !1/q, where M is the Hardy-Littlewood maximal function. As a consequence we derive the main result establishing that in the range 1 <q<p< ∞ there exists a constant C such that Z Rn Mqf(x)p w(x)dx ≤ C Z Rn |f(x)|p q M[ p q ]+1w(x)dx. Furthermore the result is sharp since M[ p q ]+1 cannot be replaced by M[ p q ]. We also show the following endpoint estimate w({x ∈ Rn : Mqf(x) > λ}) ≤ C λ Z Rn |f(x)|q Mw(x)dx, where C is a constant independent of λ. |
Funding agencies | Dirección General de Investigación Científica y Técnica (DGICYT). España |
Project ID. | PB940192 |
Citation | Pérez Moreno, C. (2000). Sharp weighted inequalities for the vector-valued maximal function. Transactions of the American Mathematical Society, 352 (7), 3265-3288. |
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