Boundedness of Hausdorff operators on Hardy spaces over homogeneous spaces of Lie groups

2021/02/19 by А. Р. Миротин, Mirotin, A. R. · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Holomorphic and Operator Theory #Advanced Banach Space Theory

paper · pdf · doi:10.48550/arxiv.2102.09859

Abstract

The aim of this note is to give the boundedness conditions for Hausdorff operators on Hardy spaces H¹ with the norm defined via (1,q) atoms over homogeneous spaces of Lie groups with doubling property and to apply results we obtain to generalized Delsarte operators and to Hausdorff operators over multidimensional spheres.

Cited by

• On the regularity of generic Hausdorff-type transformations
• Boundedness of Hausdorff-type operators with two-variable kernels on Lebesgue spaces

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