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Journal of Function Spaces and Applications
Volume 2012, Article ID 384593, 27 pages
http://dx.doi.org/10.1155/2012/384593
Research Article

New Herz Type Besov and Triebel-Lizorkin Spaces with Variable Exponents

Department of Mathematics, Hainan Normal University, Haikou 571158, China

Received 19 October 2012; Accepted 3 December 2012

Academic Editor: Baoxiang Wang

Copyright © 2012 Baohua Dong and Jingshi Xu. 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

The authors establish the boundedness of vector-valued Hardy-Littlewood maximal operator in Herz spaces with variable exponents. Then new Herz type Besov and Triebel-Lizorkin spaces with variable exponents are introduced. Finally, characterizations of these new spaces by maximal functions are given.