Carlos Mudarra

activity

20162020

collaborators

8 papers

math.CA2020

On the extension of Muckenhoupt weights in metric spaces

Emma-Karoliina Kurki, Carlos Mudarra

A theorem by Wolff states that weights defined on a measurable subset of $R^{n}$ and satisfying a Muckenhoupt-type condition can be extended into the whole space as Muckenho…

math.FA2019

Convex $C^{1}$ extensions of $1$ -jets from compact subsets of Hilbert spaces

Daniel Azagra, Carlos Mudarra

Let $X$ denote a Hilbert space. Given a compact subset $K$ of $X$ and two continuous functions $f : K \to R$ , $G : K \to X$ , we show that a necessary and sufficient condition for…

math.FA2019

Prescribing tangent hyperplanes to $C^{1, 1}$ and $C^{1, ω}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces

Daniel Azagra, Carlos Mudarra

Let $X$ denote $R^{n}$ or, more generally, a Hilbert space. Given an arbitrary subset $C$ of $X$ and a collection $H$ of affine hyperplanes of $X$ such that every…

math.FA2018

Extensions of convex functions with prescribed subdifferentials

Daniel Azagra, Juan Ferrera, Javier Gómez-Gil +1

Let $E$ be an arbitrary subset of a Banach space $X$ , $f : E \to R$ be a function, and $G : E ⇉ X^{*}$ be a set-valued mapping. We give necessary and su…

math.FA2018

Kirszbraun's theorem via an explicit formula

Daniel Azagra, Erwan Le Gruyer, Carlos Mudarra

Let $X, Y$ be two Hilbert spaces, $E$ a subset of $X$ and $G : E \to Y$ a Lipschitz mapping. A famous theorem of Kirszbraun's states that there exists $G : X \to Y$ with…

math.FA2018

Approximation of Lipschitz functions preserving boundary values

Robert Deville, Carlos Mudarra

Given an open subset $Ω$ of a Banach space and a Lipschitz function $u_{0} : Ω \to R,$ we study whether it is possible to approximate $u_{0}$ uniformly on $Ω$ by $C^{k}$ …

On the extension of Muckenhoupt weights in metric spaces

Convex C1 extensions of 1-jets from compact subsets of Hilbert spaces

Prescribing tangent hyperplanes to C1,1 and C1,ω convex hypersurfaces in Hilbert and superreflexive Banach spaces

Extensions of convex functions with prescribed subdifferentials

Kirszbraun's theorem via an explicit formula

Approximation of Lipschitz functions preserving boundary values

Convex $C^{1}$ extensions of $1$ -jets from compact subsets of Hilbert spaces

Prescribing tangent hyperplanes to $C^{1, 1}$ and $C^{1, ω}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces