On boundedness of Hausdorff-type operators on Sobolev spaces

2024/06/15 by A. R. Mirotin, Mirotin, A. R.
Mathematics · #42B35 #44A05 #44A30 #47G10 #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2406.10668

openalex publication_date 2024/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new notion of a Hausdorff-type operator on function spaces over domains in Euclidean spaces is introduced, and a sufficient condition for the boundedness of this operator on Sobolev spaces is proved. It is shown that this condition cannot be weakened in general.

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