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Journal of Function Spaces and Applications
Volume 7 (2009), Issue 2, Pages 153-166
http://dx.doi.org/10.1155/2009/465079

Atomic decompositions of Lorentz martingale spaces and applications

1School of Mathematical Science and Computing Technology, Central South University, Chang Sha 410081, China
2School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China

Received 1 November 2007

Academic Editor: Maria Carro

Copyright © 2009 Hindawi Publishing Corporation. 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

In the paper we present three atomic decomposition theorems of Lorentz martingale spaces. With the help of atomic decomposition we obtain a sufficient condition for sublinear operator defined on Lorentz martingale spaces to be bounded. Using this sufficient condition, we investigate some inequalities on Lorentz martingale spaces. Finally we discuss the restricted weak-type interpolation, and prove the classical Marcinkiewicz interpolation theorem in the martingale setting.