Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592099 | Journal of Functional Analysis | 2008 | 16 Pages |
Abstract
If X⊂Y are two classes of analytic functions in the unit disk D and θ is an inner function, θ is said to be (X,Y)-improving, if every function f∈X satisfying fθ∈Y must actually satisfy fθ∈X. This notion has been recently introduced by K.M. Dyakonov. In this paper we study the (X,Y)-improving inner functions for several pairs of spaces (X,Y). In particular, we prove that for any p∈(0,1) the (Qp,BMOA)-improving inner functions and the (Qp,B)-improving inner functions are precisely the inner functions which belong to the space Qp. Here, B is the Bloch space. We also improve some results of Dyakonov on the subject regarding Lipschitz spaces and Besov spaces.
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