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

Abstract

For 0<s<1, let {zn} be a sequence in the open unit disk such that ∑n(1−|zn|2)sδzn 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.