Related papers: Carleson measure and balayage
A Denjoy domain is a plane domain whose complement is a closed subset $E$ of the extended real line $\bar{R}$ containing $\infty$ : such a domain is called Carleson-homogeneous if there exists $C>0$ such that for all $z\in E$ and $r>0$, one…
A radial probability measure is a probability measure with a density (with respect to the Lebesgue measure) which depends only on the distances to the origin. Consider the Euclidean space enhanced with a radial probability measure. A…
This paper presents a method for finding a sparse representation of Barron functions. Specifically, given an $L^2$ function $f$, the inverse scale space flow is used to find a sparse measure $\mu$ minimising the $L^2$ loss between the…
We give several new characterizations of Caratheodory convergence of simply connected domains. We then investigate how different definitions of convergence generalize to the multiply-connected case.
The latest Belle and BaBar measurements of the inclusive B -> X_s l^+ l^- branching ratio have smaller errors and lower central values than the previous ones. We point out that these results indicate that the sign of the b -> s gamma…
We study a weighted version of Carleman's inequality via Carleman's original approach. As an application of our result, we prove a conjecture of Bennett.
We determine the sub-collections of the dyadic intervals that are able to detect the Haar type of a Banach space. The underlying dichotomy is expressed in terms of the Carleson packing condition.
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
Besides the classical distinction of correlation and dependence, many dependence measures bear further pitfalls in their application and interpretation. The aim of this paper is to raise and recall awareness of some of these limitations by…
For a large class of Cantor sets on the real-line, we find sufficient and necessary conditions implying that a set has positive (resp. null) measure for all doubling measures of the real-line. We also discuss same type of questions for…
In this paper the notion of modular cone metric space is introduced and some properties of such spaces are investigated. Also we define convex modular cone metric which takes values in CR(Y) where Y is a compact Hausdorff space. Then a…
Since the pioneering works of Jakobson and Benedicks & Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures…
In the theory of $g_\alpha$-potentials on a domain $D\subset\mathbb R^n$, $n\geqslant2$, $g_\alpha$ being the $\alpha$-Green kernel associated with the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$ of order $\alpha\in(0,n)$, $\alpha\leqslant2$,…
In this paper we study set convergence aspects for Banach spaces of vector-valued measures with divergences (represented by measures or by functions) and applications. We consider a form of normal trace characterization to establish…
We make two contributions to the problem of estimating the $L_1$ calibration error of a binary classifier from a finite dataset. First, we provide an upper bound for any classifier where the calibration function has bounded variation.…
Pearson's correlation is an important summary measure of the amount of dependence between two variables. It is natural to want to generalise the concept of correlation as a single number that measures the inter-relatedness of three or more…
Continuity of measure asserts that the measure of the union of an increasing sequence of sets is equal to the supremum of the measures of those sets. We provide counter examples in the case of uncountable unions. We construct the first…
We construct a non-doubling measure on the real line, all tangent measures of which are equivalent to Lebesgue measure.
Very precise measurements of masses and cross sections, with errors of <1%, are expected to be achievable with a future linear collider. Such an accuracy gives sensitivity at the level of quantum corrections, which therefore must be…
We give a capacitary type characterization of Carleson measures for a class of Hardy-Sobolev spaces (also known as weighted Dirichlet spaces) on the Siegel upper half-space, introduced by Arcozzi et al. This answers in part a question…