Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions
نویسندگان
چکیده
We prove an intrinsic equivalence between strong hypercontractivity (sHC) and a strong logarithmic Sobolev inequality (sLSI) for the cone of logarithmically subharmonic (LSH) functions. We introduce a new large class of measures, Euclidean regular and exponential type, in addition to all compactly-supported measures, for which this equivalence holds. We prove a Sobolev density theorem through LSH functions, and use it to prove the equivalence of (sHC) and (sLSI) for such log-subharmonic functions.
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