El principio de Calderón-Zygmund

Abstract

In this note we show some estimates for multilinear commutators with vector symbol b = (b1,...,bm) defined by the expression Tbf(x) = Z Rn2 4Ym j=1 (bj (x) − bj (y)) 3 5 K(x, y)f(y) dy, where K is the kernel of any Calderón-Zygmund operator. We generalize and sharpen both classical results from Coifman, and Coifman, Rochberg and Weiss; and also more recent results from the first author. We show that these operators are intimately related to certain appropriate Orlicz type maximal function of the form ML(log L)α where the number α is related to the symbol b.