Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.

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Abstract

Hypercontractive estimates are obtained for the Poisson semigroup on Lp(Sn). Such estimates are determined by a sharp logarithmic Sobolev inequality that relates the entropy of a function on Sn to its smoothness.

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Cite This Study

William Beckner (Mon,) studied this question.

synapsesocial.com/papers/6a230b67a3066e858357fb2b https://doi.org/https://doi.org/10.1073/pnas.89.11.4816

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