Related papers: A sharp weighted anisotropic Poincar\'e inequality…
We prove a new general Poincar\'e-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and…
We consider a type of Hardy-Sobolev inequality, whose weight function is singular on the whole domain boundary. We are concerned with the attainability of the best constant of such inequality. In dimension two, we link the inequality to a…
We study an optimal weak transport cost related to the notion of convex order between probability measures. On the real line, we show that this weak transport cost is reached for a coupling that does not depend on the underlying cost…
In this paper, we prove the anisotropic Shannon inequality for the Renyi entropy with the best constant on Folland-Stein homogeneous Lie groups. As a consequence, we also prove the optimal Shannon inequality in the same setting. Using a…
In this note we prove the anisotropic version of the Shannon inequality. This can be conveniently realised in the setting of Folland and Stein's homogeneous groups. We give two proofs: one giving the best constant, and another one using the…
Weighted fractional Poincar\'e-type inequalities are proved on John domains whenever the weights defined on the domain are depending on the distance to the boundary and to an arbitrary compact set in the boundary of the domain.
We review a method to obtain optimal Poincar\'e-Hardy-type inequalities on the hyperbolic spaces, and discuss briefly generalisations to certain classes of Riemannian manifolds. Afterwards, we recall a corresponding result on homogeneous…
In the paper, we investigate Poincare type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We derive exact and easily computable constants for some…
We prove an improved version of Poincar\'e-Hardy inequality in suitable subspaces of the Sobolev space on the hyperbolic space via Bessel pairs. As a consequence, we obtain a new Hardy type inequality with an improved constant (than the…
We prove a spanning result for vector-valued Poincar\'e series on a bounded symmetric domain. We associate a sequence of holomorphic automorphic forms to a submanifold of the domain. When the domain is the unit ball in ${\Bbb{C}}^n$, we…
Consider the Poincar\'e-Sobolev inequality on the hyperbolic space: for every $n \geq 3$ and $1 < p \leq \frac{n+2}{n-2},$ there exists a best constant $S_{n,p, \lambda}(\mathbb{B}^{n})>0$ such that $$S_{n, p,…
Firstly, we derive in dimension one a new covariance inequality of $L_{1}-L_{\infty}$ type that characterizes the isoperimetric constant as the best constant achieving the inequality. Secondly, we generalize our result to $L_{p}-L_{q}$…
Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…
We prove second and fourth order improved Poincar\'e type inequalities on the hyperbolic space involving Hardy-type remainder terms. Since theirs l.h.s. only involve the radial part of the gradient or of the laplacian, they can be seen as…
We prove sharper Strichartz estimates than expected from theoptimal dispersion bounds.
In this paper we study the best constant in a Hardy inequality for the p-Laplace operator on convex domains with Robin boundary conditions. We show, in particular, that the best constant equals $((p-1)/p)^p$ whenever Dirichlet boundary…
In this paper, we prove an optimal Heintze-Karcher-type inequality for anisotropic free boundary hypersurfaces in general convex domains. The equality is achieved for anisotropic free boundary Wulff shapes in a convex cone. As applications,…
We prove a local two-weight Poincar\'e inequality for cubes using the sparse domination method that has been influential in harmonic analysis. The proof involves a localized version of the Fefferman--Stein inequality for the sharp maximal…
In this paper, We establish the weighted Poincar\'{e} inequalities and Log-Sobolev inequalities for Cauchy distributions with optimal weight functions.
We give a new proof of the isoperimetric inequality in the plane, based on Steiner's formula for the area of a convex neighborhood. This proof establishes the isoperimetric inequality directly, without requiring that we separately establish…