A generalization of a logarithmic Sobolev inequality to the Hölder class. (English) Zbl 1242.46041

Summary: In a recent work of the author, a parabolic extension of the elliptic Ogawa type inequality has been established. This inequality has originated from the Brezis-Gallouët-Wainger logarithmic type inequalities revealing Sobolev embeddings in the critical case. In this paper, we improve the parabolic version of the 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.


46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
26D10 Inequalities involving derivatives and differential and integral operators
Full Text: DOI arXiv


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