A Carleson type measure and a family of Möbius invariant function spaces

Abstract

For $0<s<1$, let $\left\{z_n\right\}$ be a sequence in the open unit disk such that ${\sum }_n{(1-{\left|z_n\right|}^2)}^s{\delta }_{z_n}$ is an s-Carleson measure. In this paper, we consider the connections between this s-Carleson measure and the theory of Möbius invariant F(p, p-2, s) spaces by the Volterra type operator, the reciprocal of a Blaschke product, and second order complex differential equations having a prescribed zero sequence.