I obtained my PhD in Mathematics and Statistics from the University of the Basque Country at the BCAM - Basque Center for Applied Mathematics under the supervision of Carlos Pérez Moreno (Ikerbasque Research Professor, UPV/EHU and BCAM) and Luz Roncal (Ikerbasque Research Fellow, BCAM).
Here you can find my PhD thesis.
Contact:
Email: jmartinezperales(at)uma(dot)es
Websites: arXiv, ResearchGate, ORCID, Scholar, GitHub.
I have been editor at the TEMat journal promoted by the ANEM.
I am also part of the Bilbao Analysis and PDE group.
My research is focused in the study of weighted generalized Poincaré-type inequalities by means of techniques of Harmonic Analysis. More specifically, I have mainly been studying self-improving results as a tool for obtaining weighted Poincaré-Sobolev inequalities both in the Euclidean setting and the abstract context of metric measure spaces with the so-called doubling property. Fractional and classical Poincaré-Sobolev inequalities and also BMO type inequalities are among the inequalities I study.
Ritva Hurri-Syrjänen, Javier C. Martínez-Perales, Carlos Pérez, and Antti V. Vähäkangas. On the Weighted Inequality Between the Gagliardo and Sobolev Seminorms. Preprint (2023).
Javier Martinez-Perales and Carlos Perez. “Remarks on vector-valued Gagliardo and Poincaré-Sobolev type inequalities with weights”. Potentials and Partial Differential Equations. The Legacy of David R. Adams (2023).
Ritva Hurri-Syrjänen, Javier C. Martínez-Perales, Carlos Pérez, and Antti V. Vähäkangas. Degenerate fractional Poincaré-Sobolev inequalities with double extra gain. Int. Math. Res. Not. (2022). Preprint in arXiv:2201.11712v1 [math.CA] (2022).
Dariusz Kosz, Javier C. Martínez-Perales, Victoria Paternostro, Ezequiel Rela and Luz Roncal, Maximal operators on the infinite-dimensional torus. Math. Ann. (2022). Preprint in arXiv:2109.04811 [math.CA] (2021).
Javier C. Martínez-Perales, Ezequiel Rela, and Israel P. Rivera Ríos, Quantitative John-Nirenberg inequalities at different scales. Preprint in arXiv:2010.01221 [math.CA] (2020).
Javier C. Martínez-Perales, A note on generalized Poincaré-type inequalities with applications to weighted improved Poincaré-type inequalities. Ann. Acad. Sci. Fenn. Math (2021).
Eugenia Cejas, Irene Drelichman, and Javier C. Martínez-Perales, Improved fractional Poincaré type inequalities on John domains, Ark. Mat. (2019). Preprint in arXiv:1902.10578 [math.CA].
Natalia Accomazzo, Javier C. Martínez-Perales, and Israel P. Rivera-Ríos, On bloom type estimates for iterated commutators of fractional integrals, Indiana Univ. Math. J. (2020). Preprint in arXiv:1712.06923 [math.CA].
I studied my Master and Bachelor's degrees at Universidad de Málaga. Here you can find my Master and Bachelor theses:
Master Thesis: Factorización y ceros de funciones en espacios de funciones analíticas
Bachelor Thesis: La integral de Henstock-Kurzweil
Other publications:
La integral de Henstock-Kurzweil y el segundo teorema fundamental del cálculo, TEMat 1 (2017), pp. 15-23
Four different approaches to the fractional Laplacian, TEMat: monográficos, 1 (2020): Artículos de las VIII y IX Escuela-Taller de Análisis Funcional, pp. 47-60
I can barely speak Spanish. I know a little bit of English and also a tiny bit of Basque. Unfortunately I still do not know any swear word in the latter, but I know plenty of them in Italian. I am perfectly able to order a beer in all these languages, though.
This is me with Terence Tao in (probably) his happiest day ever.