Sharp Logarithmic Sobolev and related inequalities with monomial weights

We derive a sharp Logarithmic Sobolev inequality with monomial weights starting from a sharp Sobolev inequality with monomial weights. Several related inequalities such as Shannon type and Heisenberg's uncertain type are also derived. A characterization of the equality case for the Logarithmic...

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Bibliographic Details
Published in:arXiv.org 2019-07
Main Authors: Feo, Filomena, Takahashi, Futoshi
Format: Article
Language:English
Subjects:
Inequalities
Inequality
Online Access:Get full text
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Summary:We derive a sharp Logarithmic Sobolev inequality with monomial weights starting from a sharp Sobolev inequality with monomial weights. Several related inequalities such as Shannon type and Heisenberg's uncertain type are also derived. A characterization of the equality case for the Logarithmic Sobolev inequality is given when the exponents of the monomial weights are all zero or integers. Such a proof is new even in the unweighted case.
ISSN:2331-8422