Complex linear differential equations with solutions in the H2K spaces. Issue 11 (2nd November 2022) - Sun, Yu; Liu, Jinlin; Hu, Guangming
Abstract : In this paper, we give the n th derivertive criterion for functions belonging to function spaces H K 2 . Furthermore, some sufficient conditions for coefficients of the linear differential equation f ( k ) + A k − 1 ( z ) f ( k − 1 ) + ⋯ + A 1 ( z ) f ′ + A 0 ( z ) f = A k ( z ) are found such that all solutions belong to the H K 2 spaces, where A j ( z ) are analytic functions in D, j = 0, …, k .