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Journal of Function Spaces and Applications
Volume 2012, Article ID 673929, 29 pages
http://dx.doi.org/10.1155/2012/673929
Research Article

Martingale Morrey-Campanato Spaces and Fractional Integrals

1Department of Mathematics, Ibaraki University, Mito, Ibaraki 310-8512, Japan
2Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan

Received 3 March 2012; Revised 23 April 2012; Accepted 23 April 2012

Academic Editor: Dachun Yang

Copyright © 2012 Eiichi Nakai and Gaku Sadasue. 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 introduce Morrey-Campanato spaces of martingales and give their basic properties. Our definition of martingale Morrey-Campanato spaces is different from martingale Lipschitz spaces introduced by Weisz, while Campanato spaces contain Lipschitz spaces as special cases. We also give the relation between these definitions. Moreover, we establish the boundedness of fractional integrals as martingale transforms on these spaces. To do this we show the boundedness of the maximal function on martingale Morrey-Campanato spaces.