Commutators of singular integrals on spaces of homogeneous type

GLADIS PRADOLINI; OSCAR SALINAS

CZECHOSLOVAK MATHEMATICAL JOURNAL

Mathematical Institute of Sciences of the Czech Republic

Lugar: Praga; Año: 2005 vol. 57 p. 1 - 19

0011-4642

In this work we prove some sharp weighted inequalities on spaces of homoge- neous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. of Math. 103 (1976), 611{635. As a corollary, we obtain that these operators are bounded on Lp(w) when w belongs to the Muckenhoupt´s class Ap, p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fe®erman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature. we prove a weighted Fe®erman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature. class Ap, p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fe®erman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature. we prove a weighted Fe®erman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature. Lp(w) when w belongs to the Muckenhoupt´s class Ap, p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fe®erman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature. we prove a weighted Fe®erman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature. Ap, p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fe®erman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.