Search results for " space"

On singular integral and martingale transforms

2007

Linear equivalences of norms of vector-valued singular integral operators and vector-valued martingale transforms are studied. In particular, it is shown that the UMD(p)-constant of a Banach space X equals the norm of the real (or the imaginary) part of the Beurling-Ahlfors singular integral operator, acting on the X-valued L^p-space on the plane. Moreover, replacing equality by a linear equivalence, this is found to be the typical property of even multipliers. A corresponding result for odd multipliers and the Hilbert transform is given.

On the existence of at least a solution for functional integral equations via measure of noncompactness

2017

In this article, we use fixed-point methods and measure of noncompactness theory to focus on the problem of establishing the existence of at least a solution for the following functional integral equation ¶ \[u(t)=g(t,u(t))+\int_{0}^{t}G(t,s,u(s))\,ds,\quad t\in{[0,+\infty[},\] in the space of all bounded and continuous real functions on $\mathbb{R}_{+}$ , under suitable assumptions on $g$ and $G$ . Also, we establish an extension of Darbo’s fixed-point theorem and discuss some consequences.

Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces

2015

We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Question 22 and hence also Question 24 in `Thirty-three yes or no questions about mappings, measures, and metrics' by Heinonen and Semmes. The non-minimality of the Heisenberg group is shown by giving an example of an Ahlfors $4$-regular metric space $X$ having big pieces of itself such that no Lipschitz map from a subset of $X$ to the Heisenberg group has image with positive measure, and by providing a Lipschitz map from the Heisenberg group to the space $X$ having as image the whole $X$. As part of proving the above re…

Group topologies coarser than the Isbell topology

2011

Abstract The Isbell, compact-open and point-open topologies on the set C ( X , R ) of continuous real-valued maps can be represented as the dual topologies with respect to some collections α ( X ) of compact families of open subsets of a topological space X . Those α ( X ) for which addition is jointly continuous at the zero function in C α ( X , R ) are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections α ( X ) for which C α ( X , R ) is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if X is infraconsonant. Examples based on measure theoretic methods, t…

Variations of selective separability II: Discrete sets and the influence of convergence and maximality

2012

A space $X$ is called selectively separable(R-separable) if for every sequence of dense subspaces $(D_n : n\in\omega)$ one can pick finite (respectively, one-point) subsets $F_n\subset D_n$ such that $\bigcup_{n\in\omega}F_n$ is dense in $X$. These properties are much stronger than separability, but are equivalent to it in the presence of certain convergence properties. For example, we show that every Hausdorff separable radial space is R-separable and note that neither separable sequential nor separable Whyburn spaces have to be selectively separable. A space is called \emph{d-separable} if it has a dense $\sigma$-discrete subspace. We call a space $X$ D-separable if for every sequence of …

Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma

2021

We investigate existence, uniqueness and regularity for local solutions of rough parabolic equations with subcritical noise of the form $du_t- L_tu_tdt= N(u_t)dt + \sum_{i = 1}^dF_i(u_t)d\mathbf X^i_t$ where $(L_t)_{t\in[0,T]}$ is a time-dependent family of unbounded operators acting on some scale of Banach spaces, while $\mathbf X\equiv(X,\mathbb X)$ is a two-step (non-necessarily geometric) rough path of H\"older regularity $\gamma >1/3.$ Besides dealing with non-autonomous evolution equations, our results also allow for unbounded operations in the noise term (up to some critical loss of regularity depending on that of the rough path $\mathbf X$). As a technical tool, we introduce a versi…

Law and morals in the application of the public policy exception under the twin regulations 1103 and 1104 of 2016

2021

This paper discusses the interactions between fundamental principles of domestic legal systems and non-legal standards in the application of the public policy Generalklausel within the context of the twin Regulations 1103 and 1104 of 2016. In particular, this paper argues that public policy is composed of legal principles only and that there is no space for extra legal standards when the circulation of foreign deeds, decisions and laws is in discussion. This consideration has two consequences. Firstly, the role of good morals within contemporary private international law is extremely reduc

Overview of the JET preparation for deuterium-tritium operation with the ITER like-wall

2019

Documento escrito por un elevado número de autores/as, sólo se referencia el/la que aparece en primer lugar y los/as autores/as pertenecientes a la UC3M For the past several years, the JET scientific programme (Pamela et al 2007 Fusion Eng. Des. 82 590) has been engaged in a multi-campaign effort, including experiments in D, H and T, leading up to 2020 and the first experiments with 50%/50% D–T mixtures since 1997 and the first ever D–T plasmas with the ITER mix of plasma-facing component materials. For this purpose, a concerted physics and technology programme was launched with a view to prepare the D–T campaign (DTE2). This paper addresses the key elements developed by the JET programme d…

Latvijas Vēstures Institūta Žurnāls. 2012, Nr. 3 (84)

2012

Search for a Dark Leptophilic Scalar in e(+) e(-) Collisions

2020

Many scenarios of physics beyond the standard model predict the existence of new gauge singlets, which might be substantially lighter than the weak scale. The experimental constraints on additional scalars with masses in the MeV to GeV range could be significantly weakened if they interact predominantly with leptons rather than quarks. At an e+e- collider, such a leptophilic scalar (φL) would be produced predominantly through radiation from a τ lepton. We report herein a search for e+e-→τ+τ-φL, φL→ℓ+ℓ- (ℓ=e, μ) using data collected by the BABAR experiment at SLAC. No significant signal is observed, and we set limits on the φL coupling to leptons in the range 0.04<mφL<7.0 GeV. These bounds s…