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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 690258, 14 pages
http://dx.doi.org/10.1155/2013/690258
Research Article

Martingale Morrey-Hardy and Campanato-Hardy Spaces

1Department of Mathematics, Ibaraki University, Mito, Ibaraki 310-8512, Japan
2Department of Mathematics, Osaka Kyoiku University, Kashiwara, Osaka 582-8582, Japan
3Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Minami-Osawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan

Received 10 June 2013; Accepted 17 August 2013

Academic Editor: Natasha Samko

Copyright © 2013 Eiichi Nakai 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 introduce generalized Morrey-Campanato spaces of martingales, which generalize both martingale Lipschitz spaces introduced by Weisz (1990) and martingale Morrey-Campanato spaces introduced in 2012. We also introduce generalized Morrey-Hardy and Campanato-Hardy spaces of martingales and study Burkholder-type equivalence. We give some results on the boundedness of fractional integrals of martingales on these spaces.