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A class of symbols that induce bounded composition operators for Dirichlet-type spaces on the disc (2402.10759v2)
Published 16 Feb 2024 in math.CV
Abstract: In this note we study the problem of determining the holomorphic self maps of the unit disc that induce a bounded composition operator on Dirichlet-type spaces. We find a class of symbols $\varphi$ that induce a bounded composition operator on the Dirichlet-type spaces, by applying results of the multidimensional theory of composition operators for the weighted Bergman spaces of the bi-disc.