Bounded composition operators on weighted function spaces in the unit disk
Автор: Hua Shanshan, Khoi Le Hai, Tien Pham Trong
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 3 т.22, 2020 года.
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We introduce a general class of weighted spaces H(β) of holomorphic functions in the unit disk D, which contains several classical spaces, such as Hardy space, Bergman space, Dirichlet space. We characterize boundedness of composition operators Cφ induced by affine and monomial symbols φ on these spaces H(β). We also establish a sufficient condition under which the operator Cφ induced by the symbol φ with relatively compact image φ(D) in D is bounded on H(β). Note that in the setting of H(β), the characterizations of boundedness of composition operators Cφ depend closely not only on functional properties of the symbols φ but also on the behavior of the weight sequence β.
Composition operator, weighted space, weight sequence, holomorphic function, unit disk
Короткий адрес: https://sciup.org/143172450
IDR: 143172450 | DOI: 10.46698/p4238-0191-2122-t
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