Related papers: Some remarks on weighted logarithmic Sobolev inequ…

Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…

We obtain some new inequalities of Chebyshev Type.

We establish three families of Sobolev trace inequalities of orders two and four in the unit ball under higher order moments constraint, and are able to construct \emph{smooth} test functions to show all such inequalities are \emph{almost…

A note that points out the possibility to have p<1 in Sobolev type of inequalities by a use of the momomial structure of polynomials or power series. The proof is simple: Triangle angle inequality p*>1, monomial estimate from p* to exponent…

In this article we prove sharp Landau--Kolmogorov type inequalities on a class of charges defined on Lebesgue measurable subsets of a cone in $\mathbb{R}^d$, $d\geq 1$, that are absolutely continuous with respect to the Lebesgue measure. In…

Critical Sobolev-type inequality for a class of weighted Sobolev spaces on the entire space is established. We also investigate the existence of extremal function for the associated variational problem. As an application, we prove the…

We study existence results for a problem with criticical Sobolev exponent and with a positive weight.

The principal purpose of this note is to prove a logarithmic refinement of the power weighted Hardy--Rellich inequality on $n$-dimensional balls, valid for the largest variety of underlying parameters and for all dimensions $n \in…

In this paper we present a correlation inequality with respect to Cauchy type measures. To prove our inequality, we transport the problem onto the Riemannian sphere then state and solve some special cases for a spherical correlation…

In this work a local inequality is provided which bounds the distance of an integral varifold from a multivalued plane (height) by its tilt and mean curvature. The bounds obtained for the exponents of the Lebesgue spaces involved are shown…

We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations

In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley theory in the field of Fourier analysis, while there are…

The celebrated Otto calculus has established itself as a powerful tool for proving quantitative energy dissipation estimates and provides with an elegant geometric interpretation of certain functional inequalities such as the Logarithmic…

In this paper we give simple proofs for the bounds (some of them sharp) of the difference of the moduli of the second and the first logarithmic coefficient for the general class of univalent functions and for the class of convex univalent…

In this work, we study the rigidity problem for the logarithmic Sobolev inequality on a complete metric measure space $(M^n,g,f)$ with Bakry-\'Emery Ricci curvature satisfying $Ric_f\geq \frac{a}{2}g$, for some $a>0$. We prove that if…

We study the qualitative stability of two classes of Sobolev inequalities on Riemannian manifolds. In the case of positive Ricci curvature, we prove that an almost extremal function for the sharp Sobolev inequality is close to an extremal…

Let $\Omega$ be an open set in a metric measure space $X$. Our main result gives an equivalence between the validity of a weighted Hardy-Sobolev inequality in $\Omega$ and quasiadditivity of a weighted capacity with respect to Whitney…

Let $q(x)$ and $p(x)$ denote density functions on the $n$-dimensional Euclidean space, and let $p_i(\cdot|y_1,..., y_{i-1},y_{i+1},..., y_n)$ and $Q_i(\cdot|x_1,..., x_{i-1},x_{i+1},..., x_n)$ denote their local specifications. For a class…

We consider the nonlinear Schrodinger equation with defocusing, smooth, nonlinearity. Below the critical Sobolev regularity, it is known that the Cauchy problem is ill-posed. We show that this is even worse: there is a loss of regularity,…

In this paper, we prove a Sobolev and isoperimetric inequalities for submanifold in weighted manifold. Our results generalize the Hoffman-Spruck's inequalities.