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Journal of Function Spaces
Volume 2015, Article ID 104897, 11 pages
http://dx.doi.org/10.1155/2015/104897
Research Article

A Continuous Characterization of Triebel-Lizorkin Spaces Associated with Hermite Expansions

1Department of Mathematics, Linyi University, Linyi, Shandong 276005, China
2College of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing, Zhejiang 314001, China

Received 27 January 2015; Accepted 28 April 2015

Academic Editor: David R. Larson

Copyright © 2015 Shuli Gong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the properties of the Triebel-Lizorkin spaces associated with the multidimensional Hermite expansions on (). In addition to the endpoint estimates, we give the continuous characterizations of these spaces via harmonic and thermic extensions from into . Based on this result, we obtain the boundedness of Riesz transform associated with the Hermite expansions.