Mathematical Research Letters

Volume 16 (2009)

Number 1

$A_1$ bounds for Calderón-Zygmund operators related to a problem of Muckenhoupt and Wheeden

Pages: 149 – 156

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n1.a14

Authors

Andrei K. Lerner (Universidad de Sevilla)

Sheldy Ombrosi (Universidad Nacional del Sur Bahí a Blanca)

Carlos Pérez (Universidad de Sevilla)

Abstract

We obtain an $L^p(w)$ bound for Calderón-Zygmund operators $T$ when $w\in A_1$. This bound is sharp both with respect to $\|w\|_{A_1}$ and with respect to $p$. As a result, we get a new $L^{1,\infty}(w)$ estimate for $T$ related to a problem of Muckenhoupt and Wheeden.

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