Geodesic
Complex linear differential equations with solutions in weighted Dirichlet spaces and derivative Hardy spaces
Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 653-666

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DOI

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.
DOI : 10.4153/S0008439525000013
Mots-clés : Complex linear differential equation, weighted Dirichlet spaces, derivative Hardy spaces 
Lin, Qingze; Xie, Huayou. Complex linear differential equations with solutions in weighted Dirichlet spaces and derivative Hardy spaces. Canadian mathematical bulletin, Tome 68 (2025) no. 3, pp. 653-666. doi: 10.4153/S0008439525000013
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     author = {Lin, Qingze and Xie, Huayou},
     title = {Complex linear differential equations with solutions in weighted {Dirichlet} spaces and derivative {Hardy} spaces},
     journal = {Canadian mathematical bulletin},
     pages = {653--666},
     year = {2025},
     volume = {68},
     number = {3},
     doi = {10.4153/S0008439525000013},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000013/}
}
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