Endpoint Estimates of Commutators of Singular Integrals vs. Conditions on the Symbol

Abstract

Endpoint estimates of commutators Tb of singular integrals T, are studied over general spaces that include, in particular, BMO and Lipschitz spaces. We also characterize the conditions of the symbol b in order to obtain the boundedness of the commutators of all Riesz transforms between these spaces. Finally, we apply these results over several interesting known spaces.