Related papers: Logarithmic Sobolev inequality revisited

In this paper, we give a new generalization of the Bohr inequality in refined form both for bounded analytic functions, and for sense-preserving harmonic functions with analytic part being bounded.

In this paper we proved a new numerically explicit version of the P\'{o}lya--Vinogradov inequality. Our proof is based on the new ideas of V.A. Bykovskii and improves a recent inequality obtained by C. Pomerance.

We firstly describe a maximal inequality for dual Sobolev spaces W^{-1,p}. This one corresponds to a "Sobolev version" of usual properties of the Hardy-Littlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one…

In this paper, we obtain some new inequalities for functions which are introduced by Godunova and Levin.

A version of the nonlinear Hodge equations is introduced in which the irrotationality condition is weakened. An elliptic estimate for solutions is derived.

In this paper, we will show a new characterization of operator monotone functions by a matrix reverse Cauchy inequality.

A refinement of the Hardy inequality has been presented by use of superquadratic function.

We shall give a refinement of the arithmetic-geometric mean inequality.

Certain new inequalities for the sums of factorials are presented.

The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent improved Sobolev inequality derived by M. Ledoux which brings…

This is the second in our series of papers concerning some reversed Hardy--Littlewood--Sobolev inequalities. In the present work, we establish the following sharp reversed Hardy--Littlewood--Sobolev inequality on the half space $\mathbb…

This work focuses on an improved fractional Sobolev inequality with a remainder term involving the Hardy-Littlewood-Sobolev inequality which has been proved recently. By extending a recent result on the standard Laplacian to the fractional…

In this paper, new improvement of celebrated H\"older inequality by means of isotonic linear functionals is established. An important feature of the new inequality obtained in here is that many existing inequalities related to the H\"older…

In this short note, we improve the famous Reid Inequality related to linear operators.

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…

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We analyse an analog of the entropy-power inequality for the weighted entropy.

We give a new recurrent inequality on a class of vertex Folkman numbers.

We discuss sharp Sobolev inequalities for vector valued maps.

We consider two methods to establish log-Sobolev inequalities for the invariant measure of a diffusion process when its density is not explicit and the curvature is not positive everywhere. In the first approach, based on the Holley-Stroock…