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- W2078110524 abstract "We prove that the class 𝒞 ( H Λ α , H Λ β p ) = { ϕ : C ϕ ( H Λ α ) ⊂ H Λ β p } , where HΛα and H Λ β p are holomorphic Lipschitz spaces, has the f-property for p⩾1, 0<β<1: If ϕ I ∈ 𝒞 ( H Λ α , H Λ β p ) where I is an inner function, then ϕ ∈ 𝒞 ( H Λ α , H Λ β p ) Also we characterize inner functions that belong to 𝒞 ( H Λ α , H Λ β p ) for p>0, 0<α⩽1 and 0<β⩽1. The results are deduced from a new, derivative-free, characterization of 𝒞 ( H Λ α , H Λ β p ) that extends some results of Dyakonov [Acta Math. 178 (1997) 143–167.] and the author [Acta Math. 183 (1999) 141–143; J. Math. Anal. Appl., 326 (2007) 1–11]." @default.
- W2078110524 created "2016-06-24" @default.
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- W2078110524 date "2008-04-01" @default.
- W2078110524 modified "2023-09-27" @default.
- W2078110524 title "Division by inner functions in a class of composition operators on Lipschitz spaces" @default.
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- W2078110524 doi "https://doi.org/10.1112/blms/bdm114" @default.
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