Related papers: On Kedlaya type inequalities for weighted means

\begin{abstract} In this paper we state the following weighted Hardy type inequality for any functions $\varphi$ in a weighted Sobolev space and for weight functions $\mu$ of a quite general type \begin{equation*} c_{N,\mu}…

In this paper we study higher-order difference equations which can be written as follows: $$ \mathbf{J} (y_0,y_1,...)^T = \lambda^N (y_0,y_1,...)^T, $$ where $\mathbf{J}$ is a $(2N+1)$-diagonal bounded banded matrix…

Rudelson's theorem states that if for a set of unit vectors $u_i$ and positive weights $c_i$, we have that $\sum c_i u_i\otimes u_i$ is the identity operator $I$ on ${\mathbb R}^d$, then the sum of a random sample of $Cd\ln d$ of these…

This paper presents connections between Gromov's work on isoperimetry of waists and Milman's work on the $M$-ellipsoid of a convex body. It is proven that any convex body $K \subseteq \mathbb{R}^n$ has a linear image $\tilde{K} \subseteq…

A weighted U-statistic based on a random sample X_1,...,X_n has the form U_n=\sum_{1\le i,j\le n}w_{i-j}K(X_i,X_j), where K is a fixed symmetric measurable function and the w_i are symmetric weights. A large class of statistics can be…

We present both necessary and sufficient conditions to the convex closed shape $X$ such that the inequality $$ \frac{1}{|X|} \int_X f(x)\:dx \le \frac{1}{|\partial X|} \int_{\partial X} f(x)\:dx$$ is valid for every convex function $f…

We prove a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) K\"ahler manifold, assuming only the sort of weak fall-off conditions required for the mass to actually be well-defined. For ALE scalar-flat…

In this paper, we study operator mean inequalities for the weighted arithmetic, geometric and harmonic means. We give a slight modification of Audenaert's result to show the relation between Kwong functions and operator monotone functions.…

We give general conditions to state the weighted Hardy inequality \[ c\int_{\mathbb{R}^N}\frac{\varphi^2} {|x|^2}d\mu\leq\int_{\mathbb{R}^N}|\nabla \varphi |^2 d\mu+C\int_{\mathbb{R}^N} \varphi^2d\mu,\quad \varphi\in…

To a finite type knot invariant, a weight system can be associated, which is a function on chord diagrams satisfying so-called $4$-term relations. In the opposite direction, each weight system determines a finite type knot invariant. In…

Let $S_{\alpha}$ be the multilinear square function defined on the cone with aperture $\alpha \geq 1$. In this paper, we investigate several kinds of weighted norm inequalities for $S_{\alpha}$. We first obtain a sharp weighted estimate in…

Let $C$ and $K$ be centrally symmetric convex bodies in ${\mathbb R}^n$. We show that if $C$ is isotropic then \begin{equation*}\|{\bf t}\|_{C^s,K}=\int_{C}\cdots\int_{C}\Big\|\sum_{j=1}^st_jx_j\Big\|_K\,dx_1\cdots dx_s \leq c_1L_C(\log…

A matrix-valued measure $\Theta$ reduces to measures of smaller size if there exists a constant invertible matrix $M$ such that $M\Theta M^*$ is block diagonal. Equivalently, the real vector space ${\mathscr A}$ of all matrices $T$ such…

Some new Hermite-Hadamard's inequalities for h-convex functions are proved, generalizing and unifying a number of known results. Some new applications for special Means of real numbers are also derived.

The Orlicz $\left( \ell_{2},\ell_{1}\right) $-mixed inequality states that $$ \left( \sum_{j_{1}=1}^{n}\left( \sum_{j_{2}=1}^{n}\left\vert A(e_{j_{1} },e_{j_{2}})\right\vert \right) ^{2}\right) ^{\frac{1}{2}}\leq\sqrt {2}\left\Vert…

In this article, we establish weighted strong and weak type inequalities for non-commutative square functions that naturally arise in the analysis of differences between ball averages and martingale sequences within the framework of group…

Using optimal mass transport arguments, we prove weighted Sobolev inequalities of the form \[\left(\int_E |u(x)|^q\,\omega(x) \,dx\right)^{1/q}\leq K_0\,\left(\int_E |\nabla u(x)|^p\,\sigma(x)\,dx\right)^{1/p},\ \ u\in C_0^\infty(\mathbb…

Suppose that $X,Y$ are positive random variable and $m$ a numerical (commutative) mean. We prove that the inequality ${\rm E} (m(X,Y)) \leq m({\rm E} (X), {\rm E} (Y))$ holds if and only if the mean is generated by a concave function. With…

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

Let T be a bounded linear operator acting on a complex Banach space X and (\lambda_n) a sequence of complex numbers. Our main result is that if |\lambda_n|/|\lambda_{n+1}| \to 1 and the sequence (\lambda_n T^n) is frequently universal then…