Products of functions in BMO and H1 spaces on spaces of homogeneous type

Abstract

We give an extension to certain RD-space X , i.e., space of homogeneous type in the sense of Coifman and Weiss, which has the reverse doubling property, of the definition and various properties of the product of functions in BMO ( X ) and H 1 ( X ) , and functions in Lipschitz space Λ 1 p − 1 ( X ) and H p ( X ) for p ∈ ( n n + θ , 1 ] , where n and θ denote respectively the “dimension” and the order of X .