Generalized Hölder type spaces of harmonic functions in the unit ball and half space

Abstract

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Composition operators on holomorphic variable exponent spaces

“…See Section 2 for exact definitions. Such spaces were introduced and studied recently in Karapetyants and Samko 1 (see also Karapetyants and Restrepo 2 for the case of variable exponent Hölder spaces of harmonic functions in the unit ball and half space). The interest in the study of variable exponent spaces has substantially growing recently, see other studies 3,4 and references therein.…”

Holomorphic Hölder‐type spaces and composition operators

“…Here, we treat the generalized Hölder‐type spaces of holomorphic functions with prescribed behaviour near the unit circle 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 of functions with prescribed behaviour of their derivatives.…”