Related papers: On geometric constants for discrete Morrey spaces

We construct suitable metrics for two classes of topological dynamical systems (linear maps on the torus and non-invertible expansive maps on compact spaces) in order to get a lower bound for topological entropy in terms of the resulting…

We prove that for all $n\in \mathbb{N}$, there exists a constant $C_{n}$ such that for all $d \in \mathbb{N}$, for every row contraction $T$ consisting of $d$ commuting $n \times n$ matrices and every polynomial $p$, the following…

For a bounded domain $\Omega\subset \mathbb{R}^n$ and $p>n$, Morrey's inequality implies that there is $c>0$ such that $$ c\|u\|^p_{\infty}\le \int_\Omega|Du|^pdx $$ for each $u$ belonging to the Sobolev space $W^{1,p}_0(\Omega)$. We show…

All correlation measures, classical and quantum, must be monotonic under local operations. In this paper, we characterize monotonic formulas that are linear combinations of the von Neumann entropies associated with the quantum state of a…

We consider static U(1) monopole in non-commutative space. Up to the second order in the non-commutativity scale $\theta$, we find no non-trivial corrections to the Dirac solution, the monopole mass remains infinite. We argue the same holds…

We show that the perimeter of the convex hull of finitely many disks lying in the hyperbolic or Euclidean plane, or in a hemisphere does not increase when the disks are rearranged so that the distances between their centers do not increase.…

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of…

The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…

We consider a large class of geodesic metric spaces, including Banach spaces, hyperbolic spaces and geodesic $\mathrm{CAT}(\kappa)$-spaces, and investigate the space of nonexpansive mappings on either a convex or a star-shaped subset in…

For each degree p, we construct on any closed manifold a family of Riemannian metrics, with fixed volume such that any positive eigenvalues of the rough and Hodge Laplacians acting on differential p-forms converge to zero. In particular, on…

This paper provides a discrete Poincar\'e inequality in $n$ space dimensions on a simplex $K$ with explicit constants. This inequality bounds the norm of the piecewise derivative of functions with integral mean zero on $K$ and all integrals…

It is shown that if a non-autonomous system of $2n$ first-order ordinary differential equations is expressed in the form of the Hamilton equations in terms of two different sets of coordinates, $(q_{i}, p_{i})$ and $(Q_{i}, P_{i})$, then…

We show how one can use the convexity of non-commutative $L^p$ norms to bound the relative entropy between a faithful state on a von Neumann algebra and an arbitrary excitation thereof. Our results hold for general von Neumann algebras,…

This document expands upon the relationship between discrete and continuous entropy given in (Phys. Rev. Lett. 110 130407), \Violating Continuous Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements". We provide a detailed…

We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…

We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For $n\ge 2$ and $1<p<\infty$, it is shown that $\ell_\infty^n$ is representable in a Banach space $X$ if and only if it…

For dimensions $n \geq 3$, we classify singular solutions to the generalized Liouville equation $(-\Delta)^{n/2} u = e^{nu}$ on $\mathbb{R}^n \setminus \{0\}$ with the finite integral condition $\int_{\mathbb{R}^n} e^{nu} < \infty$ in terms…

Recently, Bo'az Klartag showed that arbitrary convex bodies have Gaussian marginals in most directions. We show that Klartag's quantitative estimates may be improved for many uniformly convex bodies. These include uniformly convex bodies…

We establish sharp local $C^{1,\alpha}$-regularity for weak solutions to degenerate elliptic equations of $p$-Laplacian type with data in Morrey spaces. The proof relies on the Fefferman-Phong inequality and standard tools from regularity…

The $\Lambda$-sequence spaces $\Lambda_p$ for $1< p\leq\infty$ and its generalization $\Lambda_{\hat{p}}$ for $1<\hat{p}<\infty$, $\hat{p}=(p_n)$ is introduced. The James constants and strong $n$-th James constants of $\Lambda_p$ for…