Boundedness of Projection Operator in Generalized Holomorphic and Harmonic Spaces of Functions of Hölder Type

Karapetyants, Alexey; Restrepo, Joel E.

doi:10.1007/978-3-030-26748-3_4

Cited by 2 publications

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“…Here, we treat the generalized Hölder‐type spaces

A^{ω} false(𝔻 false)

of holomorphic functions with prescribed behaviour near the unit circle

𝕋

determined by a modulus of continuity ω = ω ( h ). These type of spaces attract an attention due to numerous applications, and we refer to the books, 25,30 references therein and papers 25,30‐38 , 39 . These spaces are closely related to their counterparts in some sense, which are the generalized Besov‐type spaces

B^{ω} false(𝔻 false)

of functions with prescribed behaviour of their derivatives.…”

Section: Introductionmentioning

confidence: 99%

Holomorphic Hölder‐type spaces and composition operators

Karapetyants

Restrepo

2020

Math Methods in App Sciences

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We study boundedness and compactness of composition operators in the generalized Hölder-type space of holomorphic functions in the unit disc with prescribed modulus of continuity. We also devote a significant part of the article to outline some embeddings between such Hölder-type spaces, to discuss properties of modulus of continuity and to construct some useful examples. KEYWORDS composition operators, Hölder spaces, holomorphic functions, modulus of continuity MSC CLASSIFICATION 47B33; 46E15; 30H99 1 INTRODUCTION Let D stand for the unit disc in complex plane C. Given a holomorphic function ∶ D → D by C , we denote the linear composition operator C f(z) ∶= f• (z) = f((z)). The study of the boundedness and compactness of the composition operator C in various function spaces over the unit disc and more general domains is a classical problem studied by many researchers. Without claiming for completeness, we mention the following spaces and references: the Besov space, 1-4

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“…Here, we treat the generalized Hölder‐type spaces