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Journal of Function Spaces and Applications
Volume 2012, Article ID 148706, 15 pages
http://dx.doi.org/10.1155/2012/148706
Research Article

A Generalization of a Logarithmic Sobolev Inequality to the Hölder Class

1Mathematics Department, School of Arts and Sciences, Lebanese International University (LIU), Beirut Campus, Al-Mouseitbeh, P.O. Box 14-6404, Beirut, Lebanon
2Mathematics Department, Faculty of Sciences, Lebanese University, Hadeth, Beirut, Lebanon

Received 6 December 2010; Accepted 14 December 2010

Academic Editor: Lars Erik Persson

Copyright © 2012 H. Ibrahim. 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

In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality is originated from the Brézis-Gallouët-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical case. In this paper, we improve the parabolic version of Ogawa inequality by allowing it to cover not only the class of functions from Sobolev spaces, but also the wider class of Hölder continuous functions.