Characterizations of Morrey type spaces

Abstract

For a nondecreasing function K : [0, ∞) → [0, ∞) and 0 < s < ∞, we introduce a Morrey type space of functions analytic in the unit disk D, denoted by D s K . Some characterizations of D s K are obtained in terms of K-Carleson measures. A relationship between two spaces D s1 K and D s2 K is given by fractional order derivatives. As an extention of some known results, for a positive Borel measure µ on D, we find sufficient or necessary conditions for the embedding map I : D s K → T s K (µ) to be bounded.

Bergman-Morrey type spaces and Volterra integral operators

“…In this paper, inspired by [14,16,17,18,20], we define a new Bergman-Morrey type space A p,K as follows. Let f ∈ H(D) and 0 < p < ∞.…”