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Carlos Mudarra

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Carlos Mudarra

Marie Curie Fellow
Department of Mathematical Sciences

carlos.mudarra@ntnu.no
906 Sentralbygg 2 Gløshaugen, Trondheim
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Research

My research fields are complex, functional, and harmonic analysis, including: Ap/Bp weights, BMO functions, fractals, convex functions, approximation in Banach spaces, and Whitney-type extension problems.  

MSCA-EF Fellowship

I am the Principal Investigator of the Marie Curie project "Geometric and harmonic analysis for weights". Two-year individual research grant. Program: Marie Skłodowska-Curie Action (MSCA-EF) 2023. Horizon Europe Funding. Grant Number: 101151594

Publications

Characterizations for arbitrary Békollé-Bonami weights, (with K.-M. Perfekt), preprint (2025).

Approximation in Hölder spaces, (with T. Oikari), preprint (2024).

Weak porosity on metric measure spaces, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, to appear.

Traces of vanishing Hölder spaces, (with K. Mohanta and T. Oikari), Journal of Geometric Analysis, 35 (2025), no. 1, Paper No. 34.

Weakly porous sets and Muckenhoupt Ap distance functions, (with T.C. Anderson, J. Lehrbäck and A. Vähäkangas), Journal of Functional Analysis, 287 (2024), no. 8,  Paper No. 110558, 34 pp.

Characterizations of weak reverse Hölder inequalities on metric measure spaces, (with J. Kinnunen and E.-K. Kurki), Mathematische Zeitschrift, 301 (2022), no. 3, 2269-2290.

On the extension of Muckenhoupt weights in metric spaces, (with E.-K. Kurki), Nonlinear Analysis, 215 (2022), Paper No. 112671, 20 pp.
  
C1,ω extension formulas for 1-jets on Hilbert spaces, (with D. Azagra), Advances in Mathematics, 389 (2021), Paper No. 107928, 44 pp.
  
Kirszbraun's theorem via an explicit formula, (with D. Azagra and E. Le Gruyer), Canadian Mathematical Bulletin, 64 (2021), no. 1, 142-153.
  
Convex C1 extensions of 1-jets from compact subsets of Hilbert spaces, (with D. Azagra), Comptes Rendus. Mathématique. Académie des Sciences. Paris, 358 (2020), no. 5, 551-556.
  
Prescribing tangent hyperplanes to C1,1 and C1,ω convex hypersurfaces in Hilbert and superreflexive spaces, (with D. Azagra), Journal of Convex Analysis, 27 (2020), no. 1, 79-102.
  
Extensions of convex functions with prescribed subdifferentials, (with D. Azagra, J. Ferrera and J. Gómez-Gil), Studia Mathematica, 253 (2020), no. 2, 199-213.
  
Approximation of Lipschitz functions preserving boundary values, (with R. Deville), Journal of Optimization Theory and Applications, 182 (2019), no. 3, 885-905. 
  
Smooth convex extensions of convex functions, (with D. Azagra), Calculus of Variations and Partial Differential Equations, 58 (2019), no. 3, Paper No. 84, 27 pp.
  
Global geometry and C1 convex extensions of 1-jets, (with D. Azagra), Analysis & PDE, 12 (2019), no. 4, 1065-1099.  
  
Explicit formulas for C1,1 and C1,ωconv extensions of 1-jets in Hilbert and superreflexive spaces, (with D. Azagra and E. Le Gruyer), Journal of Functional Analysis, 274 (2018), no. 10, 3003-3032.
  
Whitney extension theorems for convex functions of the classes C1 and C1,ω, (with D. Azagra), Proceedings of the London Mathematical Society, 114 (2017), no. 1, 133-158.
  
An extension theorem for convex functions of class C1,1 on Hilbert Spaces, (with D. Azagra), Journal of Mathematical Analysis and Applications, 446 (2017), no. 2, 1167-1182.
  
Global approximation of convex functions by differentiable convex functions on Banach spaces, (with D. Azagra), Journal of Convex Analysis, 22 (2015), no. 4, 1197-1205.

 

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2025

  • Mohanta, Kaushik; Malaguilla, Carlos Mudarra Diaz; Oikari, Tuomas. (2025) Traces of Vanishing Hölder Spaces. Journal of Geometric Analysis
    Academic article

Journal publications

  • Mohanta, Kaushik; Malaguilla, Carlos Mudarra Diaz; Oikari, Tuomas. (2025) Traces of Vanishing Hölder Spaces. Journal of Geometric Analysis
    Academic article

Teaching

TMA4145 - Linear Methods (2025)

TMA4175 - Complex Analysis (2025)

MA2106 - Complex Function Theory and Differential Equations (2024) 

MA8106 - Harmonic Analysis (2024)

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