The Dunkl-Hausdorff operator is bounded on the real Hardy space

Abstract

ABSTRACTLiflyand and Móricz in Liflyand and Móricz [The Hausdorff operator is bounded on the real Hardy space . Proc Amer Math Soc. 1999;128:1391–1396; Commuting relations for Hausdorff operators and Hilbert transforms on real Hardy spaces. Acta Math Hungar. 2002;97(1–2):133–143] studied the Hausdorff operator on the real Hardy space and proved the boundedness property and the commuting relations of this operator and Hilbert transformations. The main objective of this paper is extending these results to the context of Dunkl theory.