The structure of normal Hausdorff operators on Lebesgue spaces

2018/12/06 by А. Р. Миротин, Mirotin, A. R. · 2 citations
Mathematics · #46E30 #47B15 #47B38 #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1812.02680

openalex publication_date 2018/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a generalization of Hausdorff operator and introduce the notion of the symbol of such an operator. Using this notion we describe the structure and investigate important properties (such as invertibility, spectrum, norm, and compactness) of normal generalized Hausdorff operators on Lebesgue spaces over ℝⁿ. The examples of Cesàro operators are considered.

Cited by

• On the regularity of generic Hausdorff-type transformations
• On Hausdorff operators on homogeneous spaces of locally compact groups

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