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Journal of Function Spaces
Volume 2014, Article ID 626314, 9 pages
Research Article

Atomic Decomposition of Weighted Lorentz Spaces and Operators

1Department of Mathematics, Trinity University, 1 Trinity Place, San Antonio, TX 78212, USA
2Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL 36849, USA
3Department of Sciences and Mathematics, University of South Carolina Salkehatchie, 807 Hampton Street, Walterboro, SC 24988, USA

Received 2 February 2014; Accepted 11 April 2014; Published 19 June 2014

Academic Editor: Qingying Bu

Copyright © 2014 Eddy Kwessi 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.


We obtain an atomic decomposition of weighted Lorentz spaces for a class of weights satisfying the Δ2 condition. Consequently, we study operators such as the multiplication and composition operators and also provide Hölder’s-type and duality-Riesz type inequalities on these weighted Lorentz spaces.