Abstract
This research is concerned with second-order linear differential equation f′′+A(z)f=0, where A(z) is an analytic function in the unit disc. On the one hand, some sufficient conditions for the solutions to be in α-Bloch (little α-Bloch) space are found by using exponential type weighted Bergman reproducing kernel formula. On the other hand, we find also some sufficient conditions for the solutions to be in analytic Morrey (little analytic Morrey) space by using the representation formula.
Highlights
We shall assume that the reader is familiar with the definitions of classical function spaces, for example, Hardy space, Bergman space, and Bloch space
A sufficient condition on A(z) guaranteeing that all solutions of (1) belong to BMOA is obtained in [12, Theorem 3]; here we study the condition on A(z) which guarantee that all solutions of (1) are in analytic Morrey space by using similar idea in [12, Theorem 3]
A sufficient condition on A(z) guaranteeing that all solutions of (1) are in analytic Morrey space is shown by using representation formula
Summary
We shall assume that the reader is familiar with the definitions of classical function spaces, for example, Hardy space, Bergman space, and Bloch space. They obtained some sufficient conditions on the coefficient A(z) which guarantee all solutions of (1) belong to BMOA (VMOA) space, in which some properties of Bloch space were used. Little analytic Morrey space L20,λ(D) consists of those functions f ∈ L2,λ(D) and lim
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