The Dunkl-Hausdorff operator is bounded on the real Hardy space. Issue 11 (2nd November 2019)

• Record Type: Journal Article
• Authors: Daher, Radouan; Saadi, Faouaz
• Is Part Of: Integral transforms and special functions. Volume 30:Issue 11(2019)
• Page Start: 882
• Page End: 892
• Publication Date: 2019-11-02
• Subjects: Dunkl transformation -- Dunkl-Hausdorff operator -- Riesz transformation -- Hardy space; 47G10 -- 47B38 -- 43A32 -- 42B30 -- 42B35; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2019.1636236
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: Liflyand and Móricz in Liflyand and Móricz [The Hausdorff operator is bounded on the real Hardy space H 1 ( R ) . 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.