Endpoint boundedness of commutators on spaces of homogeneous type. Issue 14 (26th October 2017) - Liu, Liguang; Chang, Der-Chen; Fu, Xing; Yang, Dachun
Abstract: Let be a space of homogeneous type in the sense of Coifman and Weiss. Let be a family of sublinear operators that include the well-known Calderón–Zygmund operator. The authors prove that the commutator [ b,   T ] is bounded from a Hardy-type subspace of to, where denotes the Lebesgue space of all integrable functions, the atomic Hardy space of Coifman and Weiss with the dual space, b is a non-constant -function and . Indeed, the space is the largest subspace in that possesses this property. The approach taken in this article adopts the bilinear decomposition theory for the product of functions in and .