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

Abstract

We obtain an L p (w) bound for Caldern-Zygmund operators T when w 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, (w) estimate for T related to a problem of Muckenhoupt and Wheeden.