Related papers: Adams inequalities on measure spaces

In this article we prove the equivalence of certain inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian with a classical inequality of Kac. Connections are made via integral transforms including those of Laplace,…

We establish various Hardy inequalities involving the distance function from submanifolds of Riemannian manifolds, where the natural weights are expressed in terms of bounds of the mean curvature of the submanifold and sectional/Ricci…

The aim of this paper is to establish some new inequalities similar to the Ostrowski's inequalities which are more generalized than the inequalities of Dragomir and Cerone. The current article obtains bounds for the deviation of a function…

We exploit a technique based on the Emden-Fowler transform to prove optimal Hardy-Rellich inequalities on cones, including the punctured space $\mathb{R}^N\setminus\{0\}$ and the half space as particular cases. We find optimal constants for…

The Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are two proximal splitting algorithms designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to…

We study the reverse triangle inequalities for suprema of logarithmic potentials on compact sets of the plane. This research is motivated by the inequalities for products of supremum norms of polynomials. We find sharp additive constants in…

In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth…

We consider nonconstant periodic constrained minimizers of semilinear elliptic equations for integro-differential operators in $\mathbb{R}$. We prove that, after an appropriate translation, each of them is necessarily an even function which…

Any oriented $4$-dimensional Einstein metric with semi-definite sectional curvature satisfies the pointwise inequality \[ \frac{|s|}{\sqrt{6}}\geq|W^+|+|W^-|, \] where $s$, $W^+$ and $W^-$ are respectively the scalar curvature, the…

We consider abstract non-negative self-adjoint operators on $L^2(X)$ which satisfy the finite speed propagation property for the corresponding wave equation. For such operators we introduce a restriction type condition which in the case of…

The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed…

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy--Littlewood--Sobolev theorem in this context. In our main result, we investigate the dependence of…

The Arnowitt-Deser-Misner (ADM) evolution equations for the induced metric and the extrinsic-curvature tensor of the spacelike surfaces which foliate the space-time manifold in canonical general relativity are a first-order system of…

We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the…

Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Gruss type inequalities in inner product spaces. Some natural applications for…

The high-order numerical analysis for fractional Laplacian via the Riesz fractional derivative, under the low regularity solution, has presented significant challenges in the past decades. To fill in this gap, we design a grid mapping…

We demonstrate the necessity of a Poincar\'e type inequality for those metric measure spaces that satisfy Cheeger's generalization of Rademacher's theorem for all Lipschitz functions taking values in a Banach space with the Radon-Nikodym…

This note is to concern a generalization to the case of twisted coefficients of the classical theory of Abelian differentials on a compact Riemann surface. We apply the Dirichlet's principle to a modified energy functional to show the…

In this paper, we establish the bounds of sharp Trudinger-Moser inequalities on Euclidean space. Let $B$ be a ball in $\mathbb{R}^n$ and $$TM(B)=\sup_{u\in{W_{0}^{1,n}(B)},\|\nabla…

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…