Sharp Weighted Endpoint Estimates for Commutators of Singular Integrals

GLADIS GUADALUPE PRADOLINI; CARLOS PÉREZ

MICHIGAN MATHEMATICAL JOURNAL

MICHIGAN MATHEMATICAL JOURNAL

Año: 2001 vol. 49 p. 23 - 37

0026-2285

The main purpose of this paper is to improve the main result in [P2] by means of a direct proof that avoids the classical good-$\lambda$ technique considered there. The good-$\lambda$ method, introduced by D. Burkholder and R. Gundy in [BG], is a powerful tool but has the disadvantage that it is essentially adapted to measures satisfying the $A_{infty}$ condition such as the Lebesgue measure. The approach we consider here is more related to the classical argument of Calderón and Zygmund for proving that singular integral operators satisfy the weak type $(1,1)$ property having the advantage that it allows to consider more general measure. The method, however, must be different since commutators of singular integral operators with $BMO$ functions are not of weak type $(1,1)$ as shown in cite[P2].