T1 Theorems on generalized Besov and Triebel-Lizorkin spaces over spaces of homogeneous type

Abstract

In this paper we extend the definition of the Besov and the Triebel-Lizorkinspaces in the context of spaces of homogeneous-type given by Han and Sawyer in[HS] . We consider, as a control of the ´local regularity ´ , functions phi(t) more general than the potentials t^alpha used in their case. We also state Tl-type theorems in these spaces. Our approach yields some new results for kernels satisfying integral regularity conditions