Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces

A. R. Mirotin

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arXiv · 2509.01757

Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces

A. R. Mirotin

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Abstract

For a class of de Branges spaces containing polynomials, sufficient and necessary conditions are given for the boundedness and compactness of the Hausdorff operators under consideration. For the Paly-Wiener spaces we reduce the study of our Hausdorff operators to classical integral ones. The operators that appeared are Carleman and therefore closeble in $L^2(\mathbb{R})$. We obtain also conditions for boundedness, compactness and nuclearity of our operators in the Paley-Wiener space as well as the conditions for their belonging to the Hilbert-Schmidt class.

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BibTeX RIS

A. R. Mirotin. 2026-03-31. Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces. https://arxiv.org/abs/2509.01757

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