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The nonlinear superposition operators between some analytic function spaces

Fangmei Sun,Hasi Wulan

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY（2023）

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Abstract
In this paper we characterize the nonlinear superposition operators mapping the space Qs into the Dirichlet-type space Vp alpha and answer basically the remaining open cases provided by Galanopoulos, Girela, and Auxiliadora M ' arquez [J. Math. Anal. Appl. 463 (2018), pp. 659-680]. Meanwhile, we give some sufficient-necessary conditions for the superposition operators between Qs spaces in all cases.
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Key words
Dirichlet-type space, superposition operator, entire function, Qs space
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