Inhomogeneous Besov and Triebel-Lizorking spaces on spaces of homogeneous type

The authors introduce the inhomogeneous Besov space and the inhomogeneous Triebel-Lizorkin space on spaces of homogeneous type: and present their atom and molecule decompositions, their dual spaces and the complex interpolation theorems. They also establishe the relation between the homogoeneous Besov space and the inhomogeneous one, and between the homogeneous Triebel-Lizorkin space and the inhomogeneous one. Moreover, they establish T1 theorems for these inhomogeneous spaces when a≠0, and apply these T1 theorems to give new characterizations of these spaces.