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Complex linear differential equations with solutions in weighted Dirichlet spaces and derivative Hardy spaces

Published online by Cambridge University Press:  06 January 2025

Qingze Lin
Affiliation:
Department of Mathematics, Shantou University, Shantou, 515063, China e-mail: gdlqz@e.gzhu.edu.cn
Huayou Xie*
Affiliation:
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

Abstract

In this article, by the use of nth derivative characterization, we obtain several some sufficient conditions for all solutions of the complex linear differential equation

$$ \begin{align*}f^{(n)}+A_{n-1}(z)f^{(n-1)}+\ldots+A_1(z)f'+A_0(z)f=A_n(z) \end{align*} $$
to lie in weighted Dirichlet spaces and derivative Hardy spaces, respectively, where $A_i(z) (i=0,1,\ldots ,n)$ are analytic functions defined in the unit disc. This work continues the lines of the investigations by Heittokangas, et al. for growth estimates about the solutions of the above equation.

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Article
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

Q.L. is supported by STU Scientific Research Initiation Grant (No. NTF24015T)

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