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• W2587432231 abstract "For 0<p<∞ and α>−1 the space of Dirichlet type Dαp consists of those functions f which are analytic in the unit disc D and satisfy ∫D(1−|z|)α|f′(z)|pdA(z)<∞. The space Dp−1p is the closest one to the Hardy space Hp among all the Dαp. Our main object in this paper is studying similarities and differences between the spaces Hp and Dp−1p (0<p<∞) regarding superposition operators. Namely, for 0<p<∞ and 0<s<∞, we characterize the entire functions φ such that the superposition operator Sφ with symbol φ maps the conformally invariant space Qs into the space Dp−1p, and, also, those which map Dp−1p into Qs and we compare these results with the corresponding ones with Hp in the place of Dp−1p. We also study the more general question of characterizing the superposition operators mapping Dαp into Qs and Qs into Dαp, for any admissible triplet of numbers (p,α,s)." @default.
• W2587432231 created "2017-02-17" @default.
• W2587432231 creator A5037127242 @default.
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• W2587432231 date "2018-07-01" @default.
• W2587432231 modified "2023-10-02" @default.
• W2587432231 title "Superposition operators, Hardy spaces, and Dirichlet type spaces" @default.
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• W2587432231 doi "https://doi.org/10.1016/j.jmaa.2018.03.044" @default.
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