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math.FA2013★ 3 cited
Strong Logarithmic Sobolev Inequalities for Log-Subharmonic Functions
Piotr Graczyk, Todd Kemp, Jean-Jacques Loeb
We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic functions. We introduce…
math.FA2008★ 1 cited
Hypercontractivity for log-subharmonic functions
Piotr Graczyk, Todd Kemp, Jean-Jacques Loeb +1
We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on $\RR^n$ and different classes of measures: Gaussian measures on $\RR^n$, symmetri…