This is an announcement for the paper "Kolmogorov compactness criterion in variable exponent Lebesgue spaces" by Humberto Rafeiro.

Abstract: The well-known Kolmogorov compactness criterion is extended to the case of variable exponent Lebesgue spaces $L^{p(\cdot)}(\overline{\Omega})$, where $\Omega$ is a bounded open set in $\mathbb R^n$ and $p(\cdot)$ satisfies some ``standard'' conditions. Our final result should be called Kolmogorov-Tulajkov Sudakov compactness criterion, since it includes the case $p_-=1$ and requires only the ``uniform'' condition.

Archive classification: math.FA

Mathematics Subject Classification: 46B50, 46E30

Remarks: 8 pages

The source file(s), kolmogorov_18_03_2009.tex: 23807 bytes, is(are) stored in gzipped form as 0903.3214.gz with size 8kb. The corresponding postcript file has gzipped size 76kb.

Submitted from: hrafeiro@ualg.pt

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