Related papers: Sharp pointwics estimate for Fock spaces

In this paper the notion of an abstract square function (estimate) is introduced as an operator X to gamma (H; Y), where X, Y are Banach spaces, H is a Hilbert space, and gamma(H; Y) is the space of gamma-radonifying operators. By the…

In this paper, we consider estimators for an additive functional of $\phi$, which is defined as $\theta(P;\phi)=\sum_{i=1}^k\phi(p_i)$, from $n$ i.i.d. random samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size…

$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler…

An estimate for the norm of selfadjoint Toeplitz operators with a radial, bounded and integrable symbol is obtained. This emphasizes the fact that the norm of such operator is strictly less than the supremum norm of the symbol. Consequences…

We consider the distance function from an arbitrary point $p$ on a flat surface, and determine the set $F_{p}$ of all \emph{farthest points} (i.e., points at maximal distance) from $p$.

We obtain sharp estimates for the localized distribution function of M\phi, when \phi belongs to Lp,\inf where M is the dyadic maximal operator. We obtain these estimates given the L1 and Lq norm, q < p and certain weak Lp-conditions.

For $p\in (1,\infty)$ and $\alpha\in\mathbb{R}$, we consider measurable functions $g$ on $\mathbb{S}^{N-1}$ that satisfy the following weighted Hardy inequality: \begin{equation}\label{abs} \int_{\mathbb{R}^N}\frac{ g…

We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…

Sharp affine fractional $L^p$ Sobolev inequalities for functions on $\mathbb R^n$ are established. The new inequalities are stronger than (and directly imply) the sharp fractional $L^p$ Sobolev inequalities. They are fractional versions of…

Approximate $p$-point Leibniz derivation formulas as well as interpolatory Simpson quadrature sums adapted to oscillatory functions are discussed. Both theoretical considerations and numerical evidence concerning the dependence of the…

Let $\Lambda$ be a uniformly discrete set and $S$ be a compact set in $R$. We prove that if there exists a bounded sequence of functions in Paley--Wiener space $PW_S$, which approximates $\delta-$functions on $\Lambda$ with $l^2-$error $d$,…

We improve local smoothing estimates for fractional Schr\"{o}dinger equations for $\alpha \in (0,1) \cup (1,\infty)$.

Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…

The purpose of this article is to develop a technique to estimate certain bounds for entropy numbers of diagonal operator on spaces of p-summable sequences for finite p greater than 1. The approximation method we develop in this direction…

We study the eigenvalues of the localization operator $S_{A, B} = P_A\mathcal{F}^{-1}P_B\mathcal{F} P_A$, where $\mathcal{F}$ is the Fourier transform and $A = cA_0, B = B_0$ for some fixed sets $A_0, B_0\subset \mathbb{R}^d$ and a large…

We consider local weak solutions to the fractional $p$-Poisson equation of order $s$, i.e. $\left( - \Delta_p\right)^s u = f$. In the range $p>1$ and $s\in \big(\frac{p-1}{p},1\big)$ we prove Calder\'on & Zygmund type estimates at the…

Let $f$ and $g$ be analytic functions on the open unit disk of the complex plane with $f/g$ belonging to the class $\mathcal{P} $ of functions with positive real part consisting of functions $p$ with $p(0)=1$ and $\operatorname{Re} p(z)>0$…

P-splines provide a flexible and computationally efficient smoothing framework and are commonly used for derivative estimation in functional data. Including an additive penalty term in P-splines has been shown to improve estimates of…

We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…

We introduce a family of discrete analytic functions, called expandable discrete analytic functions, which includes discrete analytic polynomials, and define two products in this family. The first one is defined in a way similar to the…