Carlos Mudarra

activity

20142026

C^{1}

convex extensions of

1

-jets

8 citations · 15 across the 14 of their papers we have counts for

collaborators

21 papers

math.CA2026

The sharp Whitney extension theorem for convex $C^{1}$ Lipschitz functions

Carlos Mudarra

For an arbitrary set $E \subset R^{n}$ , and functions $f : E \to R$ , $G : E \to R^{n}$ with $G$ bounded, we construct $C^{1} (R^{n})$ convex extensions $(F,…

math.CA2025

Differentiable convex extensions with sharp Lipschitz constants

Thomas Deck, Carlos Mudarra

Given a superreflexive Banach space $X$ , and a set $E \subset X$ , we characterise the $1$ -jets $(f, G)$ on $E$ that admit $C^{1, ω}$ convex extensions $(F, D F)$ to all of $X$ ; where $…

math.CA2025

Characterizations for arbitrary Békollé-Bonami weights

Carlos Mudarra, Karl-Mikael Perfekt

We precisely characterize the relationships between the reverse Hölder inequality, the Fujii-Wilson condition, the Békollé-Bonami $B_{p}$ condition, the $B_{\infty}$ …

math.CA2024

Traces of vanishing Hölder spaces

Kaushik Mohanta, Carlos Mudarra, Tuomas Oikari

For an arbitrary subset $E \subset R^{n},$ we introduce and study the three vanishing subspaces of the Hölder space $C ˙^{0, ω} (E)$ consisting of those functions for which…

math.FA2024

Approximation in Hölder Spaces

Carlos Mudarra, Tuomas Oikari

We introduce new vanishing subspaces of the homogeneous Hölder space $C ˙^{0, ω} (X, Y)$ in the generality of a doubling modulus $ω$ and normed spaces $X$ and $Y .$ For many couple…

math.CA2023

Weak porosity on metric measure spaces

Carlos Mudarra

We characterize the subsets $E$ of a metric space $X$ with doubling measure whose distance function to some negative power $dist (\cdot, E)^{- α}$ belongs to the Muckenhoupt…

math.CA2022★ 7 cited

Weakly porous sets and Muckenhoupt $A_{p}$ distance functions

Theresa C. Anderson, Juha Lehrbäck, Carlos Mudarra +1

We examine the class of weakly porous sets in Euclidean spaces. As our first main result we show that the distance weight $w (x) = dist (x, E)^{- α}$ belongs to the Mucken…

math.CA2021

Characterizations of weak reverse Hölder inequalities on metric measure spaces

Juha Kinnunen, Emma-Karoliina Kurki, Carlos Mudarra

We present ten different characterizations of functions satisfying a weak reverse Hölder inequality on an open subset of a metric measure space with a doubling measure. Among other…

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

$C^{1, ω}$ extension formulas for $1$ -jets on Hilbert spaces

Daniel Azagra, Carlos Mudarra

We provide necessary and sufficient conditions for a $1$ -jet $(f, G) : E \to R \times X$ to admit an extension $(F, \nabla F)$ for some $F \in C^{1, ω} (X)$ . Here $E$ s…

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 $C^{k}$ …

math.DG2017★ 8 cited

Global geometry and $C^{1}$ convex extensions of $1$ -jets

Daniel Azagra, Carlos Mudarra

Let $E$ be an arbitrary subset of $R^{n}$ (not necessarily bounded), and $f : E \to R$ , $G : E \to R^{n}$ be functions. We provide necessary and sufficient condition…

math.FA2017

Explicit formulas for $C^{1, 1}$ and $C_{conv}^{1, ω}$ extensions of $1$ -jets in Hilbert and superreflexive spaces

Daniel Azagra, Erwan Le Gruyer, Carlos Mudarra

Given $X$ a Hilbert space, $ω$ a modulus of continuity, $E$ an arbitrary subset of $X$ , and functions $f : E \to R$ , $G : E \to X$ , we provide necessary and sufficient conditions…

math.FA2016

An Extension Theorem for convex functions of class $C^{1, 1}$ on Hilbert spaces

Daniel Azagra, Carlos Mudarra

Let $H$ be a Hilbert space, $E \subset H$ be an arbitrary subset and $f : E \to R, G : E \to H$ be two functions. We give a nec…

math.CA2015

Whitney Extension Theorems for convex functions of the classes $C^{1}$ and $C^{1, ω}$

Daniel Azagra, Carlos Mudarra

Let $C$ be a subset of $R^{n}$ (not necessarily convex), $f : C \to R$ be a function, and $G : C \to R^{n}$ be a uniformly continuous function, with modulus of conti…

math.CA2015

Smooth convex extensions of convex functions

Daniel Azagra, Carlos Mudarra

Let $C$ be a compact convex subset of $R^{n}$ , $f : C \to R$ be a convex function, and $m \in {1, 2, ..., \infty}$ . Assume that, along with $f$ , we are given a family o…

math.FA2014

Global approximation of convex functions by differentiable convex functions on Banach spaces

Daniel Azagra, Carlos Mudarra

We show that if $X$ is a Banach space whose dual $X^{*}$ has an equivalent locally uniformly rotund (LUR) norm, then for every open convex $U \subseteq X$ , for every $\varepsilon >0…

The sharp Whitney extension theorem for convex C1 Lipschitz functions

Differentiable convex extensions with sharp Lipschitz constants

Characterizations for arbitrary Békollé-Bonami weights

Traces of vanishing Hölder spaces

Approximation in Hölder Spaces

Weak porosity on metric measure spaces

Weakly porous sets and Muckenhoupt Ap​ distance functions

Characterizations of weak reverse Hölder inequalities on metric measure spaces

On the extension of Muckenhoupt weights in metric spaces

C1,ω extension formulas for 1-jets on Hilbert 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

Global geometry and C1 convex extensions of 1-jets

Explicit formulas for C1,1 and Cconv1,ω​ extensions of 1-jets in Hilbert and superreflexive spaces

An Extension Theorem for convex functions of class C1,1 on Hilbert spaces

Whitney Extension Theorems for convex functions of the classes C1 and C1,ω

Smooth convex extensions of convex functions

Global approximation of convex functions by differentiable convex functions on Banach spaces

The sharp Whitney extension theorem for convex $C^{1}$ Lipschitz functions

Weakly porous sets and Muckenhoupt $A_{p}$ distance functions

$C^{1, ω}$ extension formulas for $1$ -jets on Hilbert spaces

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

Global geometry and $C^{1}$ convex extensions of $1$ -jets

Explicit formulas for $C^{1, 1}$ and $C_{conv}^{1, ω}$ extensions of $1$ -jets in Hilbert and superreflexive spaces

An Extension Theorem for convex functions of class $C^{1, 1}$ on Hilbert spaces

Whitney Extension Theorems for convex functions of the classes $C^{1}$ and $C^{1, ω}$