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

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(zn) is an s-Carleson measure. In this paper, we consider the connections between this s-Carleson measure and the theory of M & ouml;bius 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.(c) 2023 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.