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arXiv · 1907.03439

Sharp Logarithmic Sobolev and related inequalities with monomial weights

Filomena Feo·Futoshi Takahashi
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Abstract

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.

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Filomena Feo, Futoshi Takahashi. 2019-07-08. Sharp Logarithmic Sobolev and related inequalities with monomial weights. https://arxiv.org/abs/1907.03439

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