Related papers: Weighted Gagliardo-Nirenberg Interpolation Inequal…

We consider a class of of massless gradient Gibbs measures, in dimension greater or equal to three, and prove a decoupling inequality for these fields. As a result, we obtain detailed information about their geometry, and the percolative…

We obtain convolution inequalities in Lebesgue and Lorentz spaces with power weights when the functions involved are assumed to be radially symmetric. We also present applications of these results to inequalities for Riesz potentials of…

We prove weighted inequalities between the Gagliardo and Sobolev seminorms and also between the Marcinkiewicz quasi-norm and the Sobolev seminorm. With $A_1$ weights we improve earlier results of Bourgain, Brezis, and Mironescu.

In this article we obtain an "off-diagonal" version of the Fefferman-Stein vector-valued maximal inequality on weighted Lebesgue spaces with variable exponents. As an application of this result and the atomic decomposition developed in [12]…

In this paper, we are interested in Gaussian versions of the classical Brunn-Minkowski inequality. We prove in a streamlined way a semigroup version of the Ehrard inequality for $m$ Borel or convex sets based on a previous work by Borell.…

This note introduces bilinear estimates intended as a step towards an $L^\infty$-endpoint Kato-Ponce inequality. In particular, a bilinear version of the classical Gagliardo-Nirenberg interpolation inequalities for a product of functions is…

This paper studies the following weighted, fractional Bernstein inequality for spherical polynomials on $\sph$: \begin{equation}\label{4-1-TD-ab} \|(-\Delta_0)^{r/2} f\|_{p,w}\leq C_w n^{r} \|f\|_{p,w}, \ \ \forall f\in \Pi_n^d,…

We study a class of isoperimetric problems on $\mathbb{R}^{N}_{+} $ where the densities of the weighted volume and weighted perimeter are given by two different non-radial functions of the type $|x|^k x_N^\alpha$. Our results imply some…

We will establish the Caffarelli-Kohn-Nirenberg type inequalities with non-doubling weights being permitted. The classical Caffarelli-Kohn-Nirenberg type inequalities are categorized into non-critical and critical cases, and it is known…

In this article, we prove a weighted Hardy inequality for $1<p<+\infty$ and dimension $d\ge1$. If $p>d$, then we can deduce from our weighted Hardy inequality a Poincar\'e inequality. The proof of the weighted Hardy inequality is based on…

In this paper, we establish several improved Caffarelli-Kohn-Nirenberg and Hardy-type inequalities. Our main results are divided into two parts. In the first part, we consider the following Caffarelli-Kohn-Nirenberg inequality:…

We prove scaling invariant Gagliardo-Nirenberg type inequalities of the form $$\|\varphi\|_{L^p(\mathbb{R}^d)}\le C\|\varphi\|_{\dot H^{s}(\mathbb{R}^d)}^{\beta} \left(\iint_{\mathbb{R}^d \times \mathbb{R}^d} \frac{|\varphi (x)|^q\,|\varphi…

In this article, we look for the weight functions (say $g$) that admits the following generalized Hardy-Rellich type inequality: $ \int_{\Omega} g(x) u^2 dx \leq C \int_{\Omega} |\Delta u|^2 dx, \forall u \in \mathcal{D}^{2,2}_0(\Omega), $…

We extend our work on nonseparated interpolating sequences, originally developed for Bergman spaces with weights of the form $(1 - |z|^2)^\alpha$, to more general weights.

Using a dimension reduction argument and a stability version of the weighted Sobolev inequality on half space recently proved by Seuffert, we establish, in this paper, some stability estimates (or quantitative estimates) for a family of the…

We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.

In this paper we consider a weighted version of one dimensional discrete Hardy's Inequality on half-line with power weights of the form $n^\alpha$. Namely we consider: \begin{equation} \sum_{n=1}^\infty |u(n)-u(n-1)|^2 n^\alpha \geq…

In this paper, we establish the existence of extremals for two kinds of Stein-Weiss inequalities on the Heisenberg group. More precisely, we prove the existence of extremals for the Stein-Weiss inequalities with full weights in Theorem 1.1…

We establish a generalization to Riemannian manifolds of the Caffarelli-Kohn-Nirenberg inequality. The applied method is based on the use of conformal Killing vector fields and Enzo Mitidieri's approach to Hardy inequalities.

We prove Ehrhard's inequality using interpolation along the Ornstein-Uhlenbeck semi-group. We also provide an improved Jensen inequality for Gaussian variables that might be of independent interest.