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Journal of Function Spaces and Applications
Volume 3, Issue 1, Pages 73-89
http://dx.doi.org/10.1155/2005/192538

On small Lebesgue spaces

1C.N.R. Istitute per le Applicazioni del Calcolo “Mauro Picone”, sezione di Napoli, via P.Castellino 111, 80131 Napoli, Italy
2Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università di Napoli, via Monteoliveto, 80134 Napoli, Italy

Received 1 April 2004

Academic Editor: Pankaj Jain

Copyright © 2005 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

We consider a generalized version of the small Lebesgue spaces, introduced in [5] as the associate spaces of the grand Lebesgue spaces. We find a simplified expression for the norm, prove relevant properties, compute the fundamental function and discuss the comparison with the Orlicz spaces.