A Generalization of a Logarithmic Sobolev Inequality to the Hölder Class. (9th January 2012)

• Record Type: Journal Article
• Authors: Ibrahim, H.
• Other Names: Persson Lars Erik Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2012(2012)
• Publication Date: 2012-01-09
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2012/148706
• Languages: English
• ISSNs: 0972-6802

Abstract

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.