Some new Triebel-Lizorkin spaces on spaces of homogeneous type and their frame characterizations (Q2458343)

This paper introduces the new Triebel-Lizorkin spaces \(\dot{F}^s_{p q}(X)\) and Besov spaces \(\dot{B}^s_{p q}(X)\) on a space \(X\) of homogeneous type, then establishes their frame characterizations. Moreover, it introduces the new Triebel-Lizorkin spaces \(b\dot{F}^s_{p q}(X)\) and \(H\dot{F}^s_{p q}(X)\) associated to a given para-accretive function \(b\). Their relation is presented. It shows that \(H\dot{F}^0_{\infty 2}(X)=\dot{F}^0_{\infty 2}(X)=BMO(X)\).