A remark on a generalization of a logarithmic Sobolev inequality to the Hölder class
نویسنده
چکیده
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 the wider class of Hölder continuous functions. AMS subject classifications: 42B35, 54C35, 42B25, 39B05.
منابع مشابه
A generalization of a logarithmic Sobolev inequality to the Hölder class
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 sp...
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