# Departamento de Matematica

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# Ezequiel Rela

 Departamento de Matemática Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires E-mail: erela@dm.uba.ar Pabellón I - Ciudad Universitaria (1428) - Ciudad Autónoma de Buenos Aires Argentina

### Research

My research interests are analysis, weight theory and geometric measure theory. I collaborate with the research group "Harmonic Analysis and Banach Spaces" at Universidad de Sevilla and with the research group "Harmonic Analysis and Fractal Geometry" at Universidad de Buenos Aires.

### Publications and preprints

#### Preprints

1. Victoria Paternostro and Ezequiel Rela, Improved Buckley's theorem on LCA groups. Submitted.
2. Ioannis Parissis and Ezequiel Rela, Asymptotically sharp reverse Hölder inequalities for flat Muckenhoupt weights. Submitted.

#### Journal Papers

1. 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.
2. Teresa Luque, Carlos Pérez and Ezequiel Rela, Optimal exponents in weighted estimates without examples. Mathematical Research Letters, 22, 1 (2015), 183-201.
3. 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.
4. Carmen Ortiz-Caraballo, Carlos Pérez and Ezequiel Rela, Exponential decay estimates for Singular Integral operators. Mathematische Annalen 357, 4, (2013), pp. 1217-1243.
5. Ursula Molter and Ezequiel Rela, Small Furstenberg sets. Journal of Mathematical Analysis and Applications 400, 2, (2013) 475-486.
6. Tuomas Hytönen, Carlos Pérez and Ezequiel Rela, Sharp Reverse Hölder property for $A_{\infty}$ weights on spaces of homogeneous type. Journal of Functional Analysis 263, 12, (2012) 3883-3899.
7. 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.
8. Ursula Molter and Ezequiel Rela, Improving dimension estimates for Furstenberg-type sets. Advances in Mathematics 223, 2, (2010) 672-688.

#### Proceedings

1. 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.
2. Carlos Pérez, Carmen Ortiz-Caraballo and Ezequiel Rela, Improving bounds for singular operator via Sharp Reverse Hölder Inequality for $A_{\infty}$. 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

#### Ph.D. Thesis

Dimension estimates for Furstenberg type sets and Restriction Theorems for Hausdorff measures, at Universidad de Buenos Aires, Department of Mathematics

#### Licenciatura (Spanish)

El problema de Kakeya , at Universidad de Buenos Aires, Department of Mathematics

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