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

Abstract

Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space $H^1$ over finite-dimensional real space generalized to the case of locally compact groups that are spaces of homogeneous type. Special cases and examples of compact Lie groups, homogeneous groups (in particular the Heisenberg group) and finite-dimensional spaces over division rings are considered.

arXiv commentThe erratum is added to the previous version of the preprint

References in corpus (1)

• Weighted Morrey estimates for Hausdorff operator and its commutator on the Heisenberg group

Cited by in corpus (7)

• The structure of normal Hausdorff operators on Lebesgue spaces
• Boundedness of Hausdorff operators on Hardy spaces over homogeneous spaces of Lie groups
• Hausdorff operators on Lebesgue spaces with positive definite perturbation matrices are non-Riesz
• On Hausdorff operators on homogeneous spaces of locally compact groups
• On the boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of groups with local doubling property
• On the description of multidimensional normal Hausdorff operators on Lebesgue spaces
• Hausdorff Operators on Some Spaces of Holomorphic Functions on the Unit Disc