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Journal of Function Spaces and Applications
Volume 2013, Article ID 859402, 21 pages
http://dx.doi.org/10.1155/2013/859402
Research Article

Applications of Littlewood-Paley Theory for -Morrey Spaces to the Boundedness of Integral Operators

1School of High Technology for Human Welfare, Tokai University, 317 Nishino Numazu, Shizuoka 410-0395, Japan
2College of Economics, Nihon University, 1-3-2 Misaki-cho, Chiyoda-ku, Tokyo 101-8360, Japan
3Department of Mathematics, Ibaraki University, Mito, Ibaraki 310-8512, Japan
4Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji, Tokyo 192-0397, Japan

Received 18 March 2012; Accepted 27 November 2012

Academic Editor: Alberto Fiorenza

Copyright © 2013 Yasuo Komori-Furuya 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

The boundedness of the various operators on -Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization of -Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization of -Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators on -Lipschitz spaces is discussed.