A Continuous Characterization of Triebel-Lizorkin Spaces Associated with Hermite Expansions. (28th May 2015)

• Record Type: Journal Article
• Authors: Gong, Shuli; Ma, Bolin; Fu, Zunwei
• Other Names: Larson David R. Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2015(2015)
• Publication Date: 2015-05-28
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2015/104897
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : We study the properties of the Triebel-Lizorkin spaces associated with the multidimensional Hermite expansions onR d (d ≥ 1 ). In addition to the endpoint estimates, we give the continuous characterizations of these spaces via harmonic and thermic extensions fromR d intoR + d + 1 . Based on this result, we obtain the boundedness of Riesz transform associated with the Hermite expansions.