Related papers: A complement to the Chebyshev integral inequality
We revisit Hardy's inequality in the scope of regular Dirichlet forms following an analytical method. We shall give an alternative necessary and sufficient condition for the occurrence of Hardy's inequality. A special emphasis will be given…
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.
We establish both sufficient and necessary conditions for the validity of the so-called Hardy-Sobolev inequalities on open sets of the Euclidean space. These inequalities form a natural interpolating scale between the (weighted) Sobolev…
In this paper, we have obtained a necessary and suffcient condition for the series.
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
We give a sufficient condition for isometric actions to have the congruency of orbits, that is, all orbits are isometrically congruent to each other. As applications, we give simple and unified proofs for some known congruence results, and…
We present a necessary and sufficient condition for the topological equivalence of a continuous function on a plane to a projection onto one of coordinates.
The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya that improves Friedrichs inequality. A remarkable feature of such a proof is that…
In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result…
The paper establishes the equality condition in the I-MMSE proof of the entropy power inequality (EPI). This is done by establishing an exact expression for the deficit between the two sides of the EPI. Interestingly, a necessary condition…
A sufficient condition for existence of a solution of a differential inclusion with a uniformly bounded right-hand side that has nonempty closed (possibly nonconvex) values is obtained. An Olech-type result is obtained as a corollary. An…
We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra.
We establish new general sufficient conditions for the existence of an invariant measure for stochastic functional differential equations and for exponential or subexponential convergence to the equilibrium. The obtained conditions extend…
In this paper we give an elementary proof for Bertrand's postulate also known as Bertrand-Chebyshev theorem.
Let $f(z)=e^{-bz^2}f_1(z)$ where $b \geq 0$ and $f_1(z)$ is a real entire function of genus 0 or 1. We give a necessary and sufficient condition in terms of a sequence of inequalities for all of the zeros of $f(z)$ to be real. These…
We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials, and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves…
A P\'olya-Szeg\"o inequality for the circular rearrangement is proven, under general assumptions. In addition, sufficient conditions are given, under which all the extremals of the inequality are symmetric.
We determine the precise conditions under which any skew Schur function is equal to a Schur function over both infinitely and finitely many variables.
Askey and Gasper (1976) proved a trigonometric inequality which improves another trigonometric inequality found by M. S. Robertson (1945). Here these inequalities are reformulated in terms of the Chebyshev polynomial of the first kind $T_n$…
In this paper, we establish a new estimate (including lower and upper bounds) for an important quantity involved in the convergence analysis of smoothed aggregation algebraic multigrid methods. The new upper bound improves the existing…