Abstract
Let \(\mathbb {D}\) be the open unit disk in the complex plane \(\mathbb {C}\), and let \(\varphi \) be a holomorphic function from disk \(\mathbb {D}\) into \(\mathbb {D}\). We study the composition operator \(C_{\varphi }\) on the variable exponent Bergman space in unit disk, and prove that this operator is bounded on \(A^{p(\cdot )}(\mathbb {D})\). We give a sufficient condition for the compactness of this operator on \(A^{p(\cdot )}(\mathbb {D})\) as well.
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The authors would like to express their sincere gratitude to the anonymous referee for his/her careful reading of the manuscript.
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Morovatpoor, A., Abkar, A. Boundedness and Compactness of Composition Operators on Variable Exponent Bergman Spaces. Mediterr. J. Math. 17, 9 (2020). https://doi.org/10.1007/s00009-019-1441-8
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DOI: https://doi.org/10.1007/s00009-019-1441-8