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.