We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalities are implied by standard hypercontractive inequalities as well as by the modified log-Sobolev inequality. Our proof is based on a new comparison lemma for Dirichlet forms and an extension of the Stroock–Varopoulos inequality. A consequence of our analysis is that all simple operators L=Id−E as well as their tensors satisfy uniform reverse hypercontractive inequalities. That is, for all q \u3c p \u3c 1 and every positive valued function f for t ≥ log(1−q)/(1−p) we have ∥e−tLf∥q ≥ ∥f∥p. This should be contrasted with the case of hypercontractive inequalities for simple operators where t is known to depend not only on p and q but also on the u...
AbstractIn the line of investigation of the works by D. Bakry and M. Emery (Lecture Notes in Math., ...
AbstractFollowing the equivalence between logarithmic Sobolev inequality, hypercontractivity of the ...
AbstractWe develop a reverse entropy power inequality for convex measures, which may be seen as an a...
We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalitie...
We develop reverse versions of hypercontractive inequalities for quantum channels. By generalizing c...
The purpose of this presentation is to provide an example where improved in-formation on hypercontra...
We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on R...
For reversible Markov chains on finite state spaces, we show that the modified log-Sobolev inequalit...
AbstractWe prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functi...
The hypercontractivity is proved for the Markov semigroupassociated with a class of stochastic Hamil...
$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F fo...
We show that the Ornstein-Uhlenbeck semigroup associated with a general Poisson random measure is hy...
76 pages, 1 figureWe introduce and study a notion of Orlicz hypercontractive semigroups. We analyze ...
AbstractThe equation ut=Δp(u1/(p−1)) for p>1 is a nonlinear generalization of the heat equation whic...
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations wi...
AbstractIn the line of investigation of the works by D. Bakry and M. Emery (Lecture Notes in Math., ...
AbstractFollowing the equivalence between logarithmic Sobolev inequality, hypercontractivity of the ...
AbstractWe develop a reverse entropy power inequality for convex measures, which may be seen as an a...
We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalitie...
We develop reverse versions of hypercontractive inequalities for quantum channels. By generalizing c...
The purpose of this presentation is to provide an example where improved in-formation on hypercontra...
We prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functions on R...
For reversible Markov chains on finite state spaces, we show that the modified log-Sobolev inequalit...
AbstractWe prove strong hypercontractivity (SHC) inequalities for logarithmically subharmonic functi...
The hypercontractivity is proved for the Markov semigroupassociated with a class of stochastic Hamil...
$\mu$ being a nonnegative measure satisfying some log-Sobolev inequality, we give conditions on F fo...
We show that the Ornstein-Uhlenbeck semigroup associated with a general Poisson random measure is hy...
76 pages, 1 figureWe introduce and study a notion of Orlicz hypercontractive semigroups. We analyze ...
AbstractThe equation ut=Δp(u1/(p−1)) for p>1 is a nonlinear generalization of the heat equation whic...
We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations wi...
AbstractIn the line of investigation of the works by D. Bakry and M. Emery (Lecture Notes in Math., ...
AbstractFollowing the equivalence between logarithmic Sobolev inequality, hypercontractivity of the ...
AbstractWe develop a reverse entropy power inequality for convex measures, which may be seen as an a...