Exotic multiplicity functions and heat maximal operators in certain Dunkl settings. Issue 10 (3rd October 2018)

• Record Type: Journal Article
• Authors: Arenas, Alberto; Labarga, Edgar; Nowak, Adam
• Is Part Of: Integral transforms and special functions. Volume 29:Issue 10(2018)
• Page Start: 771
• Page End: 793
• Publication Date: 2018-10-03
• Subjects: Dunkl Laplacian -- Dunkl transform -- Dunkl harmonic oscillator -- Dunkl Ornstein-Uhlenbeck operator -- multiplicity function -- heat semigroup maximal operator; 42C10 -- 42C05 -- 42C99; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2018.1498488
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: We consider settings of the Dunkl Laplacian, the Dunkl harmonic oscillator, and the Dunkl Ornstein-Uhlenbeck operator with the underlying group of reflections isomorphic toZ 2 d . In each of these contexts, we admit all real-valued multiplicity functions, not necessarily bounded from below, and construct the corresponding 'exotic' transform or orthogonal system. This leads to new Dunkl operator-based frameworks, which generalize those yet well known, and in which harmonic analysis can reasonably be developed. To support the last claim, in all the cases we study the associated heat semigroup maximal operators and prove that they are bounded onL p, p >1, and fromL 1 to weakL 1 .