Related papers: Bernstein inequality on conic domains and triangle

The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved,…

The Wasserstein distances $W_p$ ($p\geq 1$), defined in terms of solution to the Monge-Kantorovich problem, are known to be a useful tool to investigate transport equations. In particular, the Benamou-Brenier formula characterizes the…

We develop a weighted mixed-norm $L_q(L_p)$-estimates for solutions to fractional evolution equations of the form \[ \partial_t^\alpha w(t,x) = \phi(\Delta) w(t,x) + h(t,x), \quad w(0,\cdot) = w_0, \quad t > 0, \; x \in \mathbb{R}^d, \]…

We prove the $W^{1,2}_p$-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when $p\in (1,2]$. We also consider the corresponding Neumann…

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…

In this paper we investigate continuity properties of first and second order shape derivatives of functionals depending on second order elliptic PDE's around nonsmooth domains, essentially either Lipschitz or convex, or satisfying a uniform…

We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil on…

By differentiating a concavity principle arising from the Pr\'ekopa-Leindler inequality, we obtain a statement simultaneously strengthening the weighted boundary Poincar\'e inequality and the Brascamp-Lieb variance inequality. The resulting…

We prove that for $p\in (0,1]$, the double inequality% \begin{equation*} \tfrac{1}{3p^{2}}\cos px+1-\tfrac{1}{3p^{2}}<\frac{\sin x}{x}<\tfrac{1}{% 3q^{2}}\cos qx+1-\tfrac{1}{3q^{2}} \end{equation*}% holds for $x\in (0,\pi /2)$ if and only…

Let $\omega$ and $\nu$ be radial weights on the unit disc of the complex plane, and denote $\sigma=\omega^{p'}\nu^{-\frac{p'}p}$ and $\omega_x =\int_0^1 s^x \omega(s)\,ds$ for all $1\le x<\infty$. Consider the one-weight inequality…

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

We prove a new Bernstein-type inequality for the log-likelihood function of Bernoulli variables. In contrast to classical Bernstein's inequality and Hoeffding's inequality when applied to the log-likelihood, the new bound is independent of…

Bernstein's classical inequality asserts that given a trigonometric polynomial $T$ of degree $n\geq1$, the sup-norm of the derivative of $T$ does not exceed $n$ times the sup-norm of $T$. We present various approaches to prove this…

Firstly, this paper establishes useful forms of the remainder term of Hardy-type inequalities on general domains where the weights are functions of the distance to the boundary. For weakly mean convex domains we use the resulting identities…

A Bernstein-type inequality in the standard Hardy space H^{2} of the unit disc \mathbb{D}=\{z\in\mathbb{C}:\,|z|<1\}, for rational functions in \mathbb{D} having at most n poles all outside of \frac{1}{r}\mathbb{D}, 0

The effective field, which plays the part of the vierbein in general relativity, can have topologically stable surfaces, vierbein domain walls, where the effective contravariant metric is degenerate. We consider vierbein walls separating…

In this short note we derive, for bounded domains, an upper bound for a Friedrichs type constant in a weighted Friedrichs type inequality. This upper bound generalizes a well known upper bound of the Friedrichs constant. This upper bound is…

We prove some sharp extremal distance results for functions in weighted Bergman spaces on the upper halfplane.We also prove such results in the context of bounded strictly pseudoconvex domains with smooth boundary

We present a short proof of a conjecture proposed by I. Ra\c{s}a (2017), which is an inequality involving basic Bernstein polynomials and convex functions. This proof was given in the letter to I. Ra\c{s}a (2017). The methods of our proof…

Two co-dimensional thick brane-worlds are investigated in quite general terms for two intersecting scalar fields generating the extra dimension defect. In general, when one considers two co-dimensional thick brane-worlds, the warp factor is…