Abstract
Results of Liflyand and collaborators on the boundedness of Hausdorff operators on the Hardy space H 1 over finite-dimensional real space are 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. In conclusion, we solve for the space L 2 an open question on compactness of a Hausdorff operator posed by Liflyand.
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