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

Abstract

For $0<s<1$, let $\{z_n\}$ be a sequence in the open unit disk such that ${\sum }_n(1-|z_n{|}^2{)}^s{\delta }_{z_n}$ 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.

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