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2007•Communications in Mathematical SciencesOpen access

Interpolation between logarithmic Sobolev and Poincare inequalities

Anton Arnold, Jean-Philippe Bartier, Jean Dolbeault

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Abstract

This paper is concerned with intermediate inequalities which interpolate between the logarithmic Sobolev (LSI) and the Poincaré inequalities.Assuming that a given probability measure gives rise to a LSI, we derive generalized Poincaré inequalities, improving upon the known constants from the literature.We also analyze the special case when these inequalities are restricted to functions with zero components for the first eigenspaces of the corresponding evolution operator.

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What this paper is about

This paper is concerned with intermediate inequalities which interpolate between the logarithmic Sobolev (LSI) and the Poincaré inequalities.Assuming that a given probability measure gives rise to a LSI, we derive generalized Poincaré inequalities, improving upon the known constants from the literature.We also analyze the special case when these inequalities are restricted to functions with zero components for the first eigenspaces of the corresponding evolution operator.

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Available abstract

This paper is concerned with intermediate inequalities which interpolate between the logarithmic Sobolev (LSI) and the Poincaré inequalities.Assuming that a given probability measure gives rise to a LSI, we derive generalized Poincaré inequalities, improving upon the known constants from the literature.We also analyze the special case when these inequalities are restricted to functions with zero components for the first eigenspaces of the corresponding evolution operator.

Key concepts: Poincaré inequality, Mathematics, Sobolev inequality, Poincaré conjecture, Logarithm, Sobolev space, Pure mathematics, Inequality

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