Haar type systems and Banach functions spaces on spaces of homogeneous type - Nowak, Luis Maria Ricardo (2014)
In this note we prove that the Haar type systems defined on spaces of homogeneous type are unconditional bases for a wide family of Banach function spaces. Also, we give a characterization of these spaces via Haar coefficients. The main tool used in the proof is a generalization of the technique of extrapolation of Rubio de Francia in Banach function spaces defined on spaces of homogeneous type.