On a general concept of a Hausdorff-type operator

2023/08/04 by А. Р. Миротин, Mirotin, A. R. · 2 citations
Mathematics · Computer Science · #Algebraic and Geometric Analysis #advanced mathematical theories #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2308.02388

Abstract

A unified approach to the concept of a Hausdorff operator is proposed in such a way that a number of classical and new operators feet into the given definition. Conditions are given for the boundedness of the operators under consideration in L^p and in the atomic Hardy space H¹, and their regularity property is investigated. Examples are considered. The author hopes that this approach will allow one to unify the study of a lot of extensions and analogs of the classical Hausdorff operator.

Cited by

• Hausdorff Operators on de Branges Spaces and Paley-Wiener spaces
• Boundedness of Hausdorff-type operators with two-variable kernels on Lebesgue spaces

Related

• Boundedness of multidimensional Hausdorff operators on L¹ and H¹ spaces
• The multi-parameter Hausdorff operators on H¹ and L^p
• Boundedness of Hausdorff-type operators with two-variable kernels on Lebesgue spaces
• On boundedness of Hausdorff-type operators on Sobolev spaces
• Boundedness of Hausdorff operators on Hardy spaces over homogeneous spaces of Lie groups