Hausdorff Operators on Some Spaces of Holomorphic Functions on the Unit Disc

2021/01/13 by А. Р. Миротин, Mirotin, A. R. · 4 citations
Mathematics · #46E30 #47B38 #47G10 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2101.05227

openalex publication_date 2021/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce Hausdorff operators over the unit disc and give conditions for boundedness of such operator in Bloch, Bergman, and Hardy spaces on the disc. Identity approximation by Hausdorff operators is also considered.

Cited by

• Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces
• On the regularity of generic Hausdorff-type transformations
• Boundedness of Hausdorff-type operators with two-variable kernels on Lebesgue spaces
• Hausdorff operators on weighted Bergman and Hardy spaces

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