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Journal of Function Spaces and Applications
Volume 2012 (2012), Article ID 293613, 10 pages
http://dx.doi.org/10.1155/2012/293613
Research Article

A Note on Multiplication and Composition Operators in Lorentz Spaces

1Trinity University, One Trinity Place, San Antonio, TX 78212, USA
2US Air Force Academy, Colorado Springs, CO 80840, USA
3Department of Mathematics and Statistics, Auburn University, 221 Parker Hall, Auburn, AL 36849, USA

Received 6 February 2012; Accepted 21 June 2012

Academic Editor: Gestur Ólafsson

Copyright © 2012 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.

Abstract

we revisit the Lorentz spaces 𝐿 ( 𝑝 , 𝑞 ) for 𝑝 > 1 , 𝑞 > 0 defined by G. G. Lorentz in the nineteen fifties and we show how the atomic decomposition of the spaces 𝐿 ( 𝑝 , 1 ) obtained by De Souza in 2010 can be used to characterize the multiplication and composition operators on these spaces. These characterizations, though obtained from a completely different perspective, confirm the various results obtained by S. C. Arora, G. Datt and S. Verma in different variants of the Lorentz Spaces.