A Note on Composition Operators Acting on Holomorphic Sobolev Spaces
نویسنده
چکیده
A holomorphic self-map φ of the unit disk is constructed such that the composition operator induced by φ is bounded on the Hardy-Sobolev space H1 2 of order 2 as well as on the ordinary holomorphic Lipschitz space Lip1 but unbounded on the Zygmund class Λ1. Among these three function spaces we have embedding relations H1 2 ⊂ Lip1 ⊂ Λ1. So, the main points here are that our construction provides a composition operator which is bounded on smaller spaces, but not on a larger space and that all the function spaces involved are standard ones.
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