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

Abstract

The aim of this note is to give the boundedness conditions for Hausdorff operators on Hardy spaces $H^1$ 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.

arXiv comment13 pages. arXiv admin note: text overlap with arXiv:2006.03281

References in corpus (1)

• Boundedness of Hausdorff operators on Hardy spaces $H^1$ over locally compact groups