Research

Publications and preprints:

• E. Alvarado, T. Merchán, L. Naples, On the problem of parametrizing Hölder curves, in preparation.

• G. Curbera, T. Merchán, Study of the finite Hilbert transform acting on $L^\infty((-1,1))$, in preparation.

• T. Merchán, F. Nazarov, A relevant example of self-contracted curves, preprint, 2023.

• T. Merchán, Robin problem on Lipschitz domains: regularity and harmonic measure, preprint, 2023.

• E. Alvarado, L. Catalano, T. Merchán, L. Naples, Asympototics of maximum distance minimizers, submitted for publication in RACSAM (2023), https://arxiv.org/abs/2309.0805.

• L. Catalano, T. Merchán, On rational functional identities, Commun. Algebra (2023), DOI:  10.1080/00927872.2023.2247488.

• B. Jaye, T. Merchán, The Huovinen transform and rectifiability of measures,  Advances in Mathematics, Volume 400, (2022), 108297.

• B. Jaye, T. Merchán, Small local action of singular integrals on spaces of non-homogeneous type. Rev. Mat. Iberoam. 36 (2020), no. 7, 2183–2207.

• B. Jaye, T. Merchán, On the problem of existence in principal value of a Calderón-Zygmund operator on a space of non-homogeneous type. Proc. London Math. Soc. 121 (2020), 152–176.