On the boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of groups with local doubling property

TL;DR

This paper establishes conditions under which Hausdorff operators are bounded on real Hardy spaces over certain homogeneous spaces, including the hyperbolic plane, expanding understanding of operator behavior in these contexts.

Contribution

It provides new boundedness criteria for Hausdorff operators on $H^1$ spaces over homogeneous groups with local doubling, including specific analysis on the hyperbolic plane.

Findings

Boundedness conditions for Hausdorff operators on $H^1$ spaces.

Application to the hyperbolic plane case.

Extension to homogeneous spaces with local doubling property.

Abstract

We give conditions for boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of locally compact groups with local doubling property. The special case of the hyperbolic plane is considered.