Journal of Function Spaces

Journal of Function Spaces / 2009 / Article

Open Access

Volume 7 |Article ID 465079 | 14 pages | https://doi.org/10.1155/2009/465079

Atomic decompositions of Lorentz martingale spaces and applications

Academic Editor: Maria Carro
Received01 Nov 2007

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.

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.


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