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Journal of Function Spaces and Applications
Volume 2, Issue 1, Pages 55-69
http://dx.doi.org/10.1155/2004/502312

A trace inequality for generalized potentials in Lebesgue spaces with variable exponent

1University of Sussex, Centre for Math. Anal. & Appl., Brighton BN1 9QH, Sussex, UK
2A. Razmadze Mathematical Institute, Georgian Academy of Sciences, 1, M. Aleksidze St, 380093 Tbilisi, Georgia

Received 1 May 2003

Academic Editor: Vladimir Stepanov

Copyright © 2004 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

A trace inequality for the generalized Riesz potentials Iα(x) is established in spaces Lp(x) defined on spaces of homogeneous type. The results are new even in the case of Euclidean spaces. As a corollary a criterion for a two-weighted inequality in classical Lebesgue spaces for potentials Iα(x) defined on fractal sets is derived.