Linear Differential Equations with Solutions in the Dirichlet Type Subspace of the Hardy Space

Abstract

Abstract Sufficient conditions for the analytic coefficients of the linear differential equation are found such that all solutions belong to a given -space, or to the Dirichlet type subspace D p of the classical Hardy space H p , where 0 < p ≤ 2. For 0 < q < ∞, the space consists of those functions f , analytic in the unit disc D , for which | f ( z )|(1 – | z | 2 ) q is uniformly bounded in D , and f ∈ D p if the integral ∫ D |f′(z)| p (1 – |z| 2 ) p–1 dσ z converges.