Localized versions of function spaces and generic results

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:465

Article

Lygkonis, Dimitris¹  Nestoridis, Vassilis¹ 

[1] Univ Athens, Dept Math, Athens 15784, Greece

关键词: Bounded holomorphic functions;    Bergman spaces;    Mergelyan's theorem;    Baire category theorem;    Non-extendable functions;    Nowhere differentiable functions;   

DOI  :  10.1016/j.jmaa.2018.05.039

来源: Elsevier

【 摘 要 】

We consider generalizations of classical function spaces by requiring that a holomorphic in Omega function satisfies some property when we approach from Omega, not the whole boundary partial derivative Omega, but only a part of it. These spaces endowed with their natural topology are Frechet spaces. We prove some generic non-extendability results in such spaces and generic nowhere differentiability on the corresponding part of partial derivative Omega. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free