Research
Research Interests
My research interests are analysis, weight theory and geometric measure theory. In particular, I am interested in Furtenberg and Kakeya type problems related to general Hausdorff measures. I am also working on degenerate (weighted) Poincaré-Sobolev inequalites and related BMO problems.
I am a member of the research group "Harmonic Analysis and Fractal Geometry" at Universidad de Buenos Aires.
Publications
Carlos Pérez and Ezequiel Rela. A tribute to Pola Harboure: Isoperimetric inequalities and the HMS extrapolation theorem. To appear in Revista de la Unión Matemática Argentina.
Abhishek Ghosh and Ezequiel Rela. Weighted Inequalities for Fractional maximal functions on the infinite rooted k-ary tree. To appear in the Journal of Geometric Analysis.
Javier Martínez Perales, Ezequiel Rela and Israel P. Rivera-Ríos. Quantitative John-Nirenberg inequalities at different scales. To appear in Revista Matemática Complutense.
Darius Kosz, Javier Martínez Perales, Victoria Paternostro, Luz Roncal and Ezequiel Rela. Maximal operators on the infinite-dimensional torus. To appear in Mathematische Annalen.
Maria Eugenia Cejas, Carolina Mosquera, Carlos Pérez and Ezequiel Rela. Some non-standard biparametric Poincaré type inequalities through harmonic analysis. To appear in Journal of Fourier Analysis and Applications.
Javier Canto, Carlos Pérez and Ezequiel Rela, Minimal conditions for BMO. Journal of Functional Analysis, Volume 282, Issue 2, 2022.
María Eugenia Cejas, Carolina Mosquera, Carlos Pérez and Ezequiel Rela, Self-improving Poincaré-Sobolev type functionals in product spaces. To appear in Journal d'Analyse Mathématique.
Sheldy Ombrosi, Carlos Pérez, Israel Rivera Ríos and Ezequiel Rela, A note on generalized Fujii-Wilson conditions and BMO spaces. Israel J. Math. 238 (2020), no. 2, 571–591.
Andrea Olivo and Ezequiel Rela, Weighted estimates for maximal functions associated to skeletons. J. Geom. Anal. 30 (2020), no. 4, 4407-4426.
Carlos Pérez and Ezequiel Rela, Degenerate Poincaré-Sobolev inequalities. Trans. Amer. Math. Soc. 372, 9 (2019), 6087–6133.
Victoria Paternostro and Ezequiel Rela, Improved Buckley's theorem on LCA groups. Pacific Journal of Mathematics, 299, 1 (2019), 171-189.
Ioannis Parissis and Ezequiel Rela, Asymptotically sharp reverse Hölder inequalities for flat Muckenhoupt weights. Indiana University Mathematical Journal, 67, 6, (2018), 2363-2391.
Teresa Luque, Carlos Pérez and Ezequiel Rela, Reverse Hölder Property for strong weights and general measures. Journal of Geometric Analysis, 27, 1 (2017), 162-182.
Teresa Luque, Carlos Pérez and Ezequiel Rela, Optimal exponents in weighted estimates without examples. Mathematical Research Letters, 22, 1 (2015), 183-201.
Carlos Pérez and Ezequiel Rela, A new quantitative two weight theorem for the Hardy-Littlewood maximal operator. Proceedings of the American Mathematical Society 143, 2, (2015), 641-655.
Carmen Ortiz-Caraballo, Carlos Pérez and Ezequiel Rela, Exponential decay estimates for Singular Integral operators. Mathematische Annalen 357, 4, (2013), pp. 1217-1243.
Ursula Molter and Ezequiel Rela, Small Furstenberg sets. Journal of Mathematical Analysis and Applications 400, 2, (2013) 475-486.
Tuomas Hytönen, Carlos Pérez and Ezequiel Rela, Sharp Reverse Hölder property for A∞ weights on spaces of homogeneous type. Journal of Functional Analysis 263, 12, (2012) 3883-3899.
Ursula Molter and Ezequiel Rela, Furstenberg-type sets for a fractal set of directions. Proceedings of the American Mathematical Society 140, 8, (2012) 2753-2765.
Ursula Molter and Ezequiel Rela, Improving dimension estimates for Furstenberg-type sets. Advances in Mathematics 223, 2, (2010) 672-688.
Proceedings
Ezequiel Rela, Refined size estimates for Furstenberg sets via Hausdorff measures: a survey of some recent results. Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. 22nd International Workshop in Operator Theory and its Applications (IWOTA), Sevilla, July 2011. Series: Operator Theory: Advances and Applications, Vol. 236, pp. 421-454. (2013) Birkhäuser.
Carlos Pérez, Carmen Ortiz-Caraballo and Ezequiel Rela, Improving bounds for singular operator via Sharp Reverse Hölder Inequality for A∞. Advances in Harmonic Analysis and Operator Theory. The Stefan Samko Anniversary Volume. Series: Operator Theory: Advances and Applications, Vol. 229, pp. 303-321. (2013) Birkhäuser
You can find my Ph.D. thesis here (in English) and my M.Sc. thesis here (in Spanish).