Journal of Function Spaces

Journal of Function Spaces / 2004 / Article

Open Access

Volume 2 |Article ID 502312 | https://doi.org/10.1155/2004/502312

David E. Edmunds, Vakhtang Kokilashvili, Alexander Meskhi, "A trace inequality for generalized potentials in Lebesgue spaces with variable exponent", Journal of Function Spaces, vol. 2, Article ID 502312, 15 pages, 2004. https://doi.org/10.1155/2004/502312

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

Academic Editor: Vladimir Stepanov
Received01 May 2003

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.

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.


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