Related papers: On Logarithmic Sobolev Inequality for the Noncommu…

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.

In this paper we show that in the case of noncommutative two-tori one gets in a natural way simple structures which have analogous formal properties as Hopf algebra structures but with a deformed multiplication on the tensor product.

In this note we give a simple, dimension independent, proof of the logarithmic Sobolev inequality on the Heisenberg groups $H_n=\R^{2n+1}$ using the measure preserving transformations of the Brownian motion. We have corrected some serious…

We derive weighted log-Sobolev inequalities from a class of super Poincar\'e inequalities. As an application, the Talagrand inequality with larger distances are obtained. In particular, on a complete connected Riemannian manifold, we prove…

We define and study analogues of exponentials for functions on noncommutative two-tori that depend on a choice of a complex structure. The major difference with the commutative case is that our noncommutative exponentials can be defined…

We study a class of logarithmic Sobolev inequalities with a general form of the energy functional. The class generalizes various examples of modified logarithmic Sobolev inequalities considered previously in the literature. Refining a…

We give an alternative proof to Wu's logarithmic Sobolev inequality for the Poisson measure on the nonnegative integers using a stochastic variational formula for entropy. We show that this approach leads to improvement of Wu's inequality…

We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case $p=n\geq2.$ In this paper we provide an optimal Sobolev-type improvement of this substitute, analogous to the…

We prove a categorical version of the Torelli theorem for cubic threefolds. More precisely, we show that the non-trivial part of a semi-orthogonal decomposition of the derived category of a cubic threefold characterizes its isomorphism…

We define analogues of homogeneous coordinate algebras for noncommutative two-tori with real multiplication. We prove that the categories of standard holomorphic vector bundles on such noncommutative tori can be described in terms of graded…

Properties of (most general) non-commutative torsors or A-B torsors are analysed. Starting with pre-torsors it is shown that they are equivalent to a certain class of Galois extensions of algebras by corings. It is shown that a class of…

We give a very concise proof of Ornstein's $L^1$ non-inequality for first- and second-order operators in two dimensions. The proof just needs a two-dimensional laminate supported on three points.

We show that the convolution of a compactly supported measure on $\mathbb{R}$ with a Gaussian measure satisfies a logarithmic Sobolev inequality (LSI). We use this result to give a new proof of a classical result in random matrix theory…

We prove an inequality for polynomials applied in a symmetric way to non-commuting operators.

In this paper, we present a novel proof of the uniform Bogomolov conjecture for algebraic tori. To do this, we introduce a definition of non-degenerate subvarieties applicable to a family of algebraic tori and establish an equidistribution…

We prove the analogue of Weyl's law for a noncommutative Riemannian manifold, namely the noncommutative two torus $\mathbb{T}_\theta^2$ equipped with a general translation invariant conformal structure and a Weyl conformal factor. This is…

We provide a proof of the sharp log-Sobolev inequality on a compact interval.

We prove logarithmic Sobolev inequalities for semi-direct product operators (see definition in Section 1). We apply our main results to examples of operators and provide some applications to ultracontractive bounds of semigroups. Hardy's…

Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincar\'e or logarithmic Sobolev inequalities. Moreover an alternative method using the…

We prove a logarithmic Sobolev trace inequality in a gaussian space and we study the trace operator in the weighted Sobolev space W^{1,p}(\Omega,\gamma) for sufficiently regular domain. We exhibit examples to show the sharpness of the…