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Between Sobolev and Poincaré

Rafał Latała·Krzysztof Oleszkiewicz
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Abstract

We establish a family of functional inequalities interpolating between the classical logarithmic Sobolev and Poincaré inequalities. We prove that they imply the concentration of measure phenomenon intermediate between Gaussian and exponential. Our bounds are close to optimal.

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Rafał Latała, Krzysztof Oleszkiewicz. 2000-03-07. Between Sobolev and Poincaré. https://doi.org/10.1007/bfb0107213

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