**Research
**

CSIC - UAM - UC3M - UCM Consejo Superior de Investigaciones Científicas Despacho 404 |
91 299 97 84 |

**Ph. D. Thesis**(avialable upon request, only in Spanish)

**Research Interests**- Harmonic Analysis
- Calderón-Zygmund Theory
- Weighted and vector-valued inequalities
- Function spaces
- PDE's

**Publications**(the PDF files below may slightly differ from the published versions)*A new characterization of chord-arc domains*, (with J. Azzam, S. Hofmann, K. Nyström and T. Toro). J. Eur. Math. Soc. (JEMS). PDF*Self-improving properties for abstract Poincaré type inequalities,*(with F. Bernicot). Trans. Amer. Math. 367, no. 7, (2015), 4793-4835. PDF*Dyadic harmonic analysis beyond doubling measures*(with L.D. López-Sánchez and J. Parcet). Adv. Math. 267 (2014), 44-93. PDF*Uniform rectifiability and harmonic measure I: Uniform rectifiability implies Poisson kernels in \(L^p\),*(with S. Hofmann). Ann. Sci. École Norm. Sup. 47 (2014), no. 3, 577-654. PDF*Uniform rectifiability and harmonic measure II: Poisson kernels in \(L^p\) imply uniform rectifiability,*(with S. Hofmann and I. Uriarte-Tuero). Duke Math. J. 163 (2014), no. 8, 1601-1654. PDF*Uniform Rectifiability and Harmonic Measure III: Riesz transform bounds imply uniform rectifiability of boundaries of 1-sided NTA domains,*(with S. Hofmann and S. Mayboroda), Int. Math. Res. Not. 2014 (2014), no. 10, 2702-2729. PDF*The higher order regularity Dirichlet problem for elliptic systems in the upper-half space*(with D. Mitrea, I. Mitrea and M. Mitrea). Harmonic Analysis and Partial Differential Equations. Proceedings of the 9th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, June 11-15, 2012, Contemporary Mathematics 612 (2014), 123-141. PDF*Calderón-Zygmund operators associated to matrix-valued kernels*(with G. Hong, L.D. López-Sánchez and J. Parcet), Int. Math. Res. Not. 2014 (2014), no. 5, 1221-1252. PDF*Self-improvement of Poincaré type inequalities associated with approximations of the identity and semigroups,*(with A. Jiménez-del-Toro), Potential Anal. 38 (2013), no. 3, 805-841. PDF*Weighted norm inequalities on graphs,*(with N. Badr), J. Geom. Anal. 22 (2012), no. 4, 1173-1210. PDF*Vertical versus conical square functions,*(with P. Auscher and S. Hofmann). Trans. Amer. Math. Soc. 364 (2012), no. 10, 5469-5489. PDF*Sharp weighted estimates for classical operators,*(with D. Cruz-Uribe and C. Pérez). Adv. Math. 229 (2012), no. 1, 408-441. PDF*\(A_\infty\) estimates via extrapolation of Carleson measures and applications to divergence form elliptic operators*, (with S. Hofmann), Trans. Amer. Math. Soc. 364 (2012), no. 1, 65-101. PDF*Weights, extrapolation and the theory of Rubio de Francia,*(with D. Cruz-Uribe and C. Pérez). Operator Theory: Advances and Applications, 215. BirkhĂ¤user/Springer Basel AG, Basel, 2011. xiv+280 pp. ISBN: 978-3-0348-0071-6. LINK*\(L^p\) self-improvement of generalized Poincaré inequalities in spaces of homogeneous type,*(with A. Jiménez-del-Toro and N. Badr). J. Funct. Anal. 260 (2011), no. 11, 3147-3188. PDF*Quantifying democracy of wavelet bases in Lorentz spaces*, (with E. Hernández and M. de Natividade), Constr. Approx. 33 (2011), no. 1, 1-14. PDF*A note on \(A_\infty\) estimates via extrapolation of Carleson measures*, (with S. Hofmann), The AMSI-ANU Workshop on Spectral Theory and Harmonic Analysis, ANU, Canberra, 13-17 July, 2009, Proceedings of the Centre for Mathematics and its Applications 44 (2010), 143-166. PDF*Sharp weighted estimates for approximating dyadic operators,*(with D. Cruz-Uribe and C. Pérez), Electron. Res. Announc. Math. Sci. 17 (2010), 12-19. PDF*Weighted norm inequalities, off-diagonal estimates and elliptic operators*, (with P. Auscher), Harmonic Analysis and Partial Differential Equations. Proceedings of the 8th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, June 16-20, 2008, Contemporary Mathematics 505 (2010), 61-83. PDF*Generalized Hörmander's conditions and weighted endpoint estimates*, (with M. Lorente, C. Pérez and M.S. Riveros), Studia Math. 195 (2009), no. 2, 157-192. PDF*Multilinear Extrapolation and applications to the bilinear Hilbert transform,*(with M.J. Carro, L. Grafakos and F. Soria), J. Math. Anal. Appl. 357 (2009), no. 2, 479-497. PDF*Weighted norm inequalities for fractional operators*, (with P. Auscher), Indiana Univ. Math. J. 57 (2008), no. 4, 1845-1870. PDF*Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part IV: Riesz transforms on manifolds and weights*, (with P. Auscher), Math. Z. 260 (2008), no. 3, 527-539. PDF*Generalized Hörmander's conditions, commutators and weights*, (with M. Lorente, M.S. Riveros and A. de la Torre), J. Math. Anal. Appl. 342 (2008), no. 2, 1399-1425. PDF*Wavelets, Orlicz spaces, and greedy bases,*(with G. Garrigós and E. Hernández), Appl. Comput. Harmon. Anal. 24 (2008), no. 1, 70-93. PDF*Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture*, (with D. Cruz-Uribe and C. Pérez), Adv. Math. 216 (2007), no. 2, 647-676. PDF*Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part II: Off-diagonal estimates on spaces of homogeneous type*, (with P. Auscher), J. Evol. Equ. 7 (2007), 265-316. PDF*Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights*, (with P. Auscher), Adv. Math. 212 (2007), no. 1, 225-276. PDF*Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part III: Harmonic Analysis of elliptic operators*, (with P. Auscher), J. Funct. Anal. 241 (2006), 703-746. PDF*Extrapolation with weights, Rearrangement Invariant Function Spaces, Modular inequalities and applications to Singular Integrals*, (with G.P. Curbera, J. García-Cuerva and C. Pérez),*The boundedness of classical operators on variable \(L^p\) spaces*, (with D. Cruz-Uribe, A. Fiorenza and C. Pérez), Ann. Acad. Sci. Fenn. Math. 31 (2006), 239-264. PDF*Extensions of Rubio de Francia's extrapolation theorem,*(with D. Cruz-Uribe and C. Pérez), Proceedings of the 7th International Conference on Harmonic Analysis and Partial Differential Equations (El Escorial 2004), Collect. Math. 2006, 195-231. PDF*Weighted weak-type inequalities and a conjecture of Sawyer*, (with D. Cruz-Uribe and C. Pérez), Int. Math. Res. Not.30 (2005), no. 5, 1849-1871. PDF*Weighted norm inequalities for maximally modulated operators*, (with L. Grafakos and F. Soria), Math. Ann. 331 (2005), no. 2, 359-394. PDF*Lack of natural weighted estimates for some singular integral operators*, (with C. Pérez and R.Trujillo-González), Trans. Amer. Math. Soc. 357 (2005), no. 1, 385-396. PDF*Weighted norm inequalities for singular integral operators,*Seminar of Mathematical Analysis (Malaga/Seville, 2003/2004), 119-129, Colecc. Abierta 71, Univ. Sevilla Secr. Publ., Seville, 2004. PDF*Weighted norm inequalities and extrapolation*, Seminar of Mathematical Analysis (Malaga/Seville, 2003/2004), 131-149, Colecc. Abierta 71, Univ. Sevilla Secr. Publ., Seville, 2004. PDF*Extrapolation from*, (with D. Cruz-Uribe and C. Pérez), J. Funct. Anal. 213 (2004), 412-439. PDF*\(A_\infty\)*weights and applications*Fractional integrals, potential operators and two-weight, weak type norm inequalities on spaces of homogeneous type*, J. Math. Anal. Appl. 294 (2004), no. 1, 223-236. PDF*Extrapolation of weighted norm inequalities for multivariable operators and applications*, (with L. Grafakos), J. Geom. Anal.14 (2004), no. 1, 19-46. PDF*Sharp maximal functions associated with approximations of the identity in spaces of homogeneous type and applications,*Studia Math.161 (2004), 113-145. PDF*\(L^p\) bounds for Riesz Transforms and Square Roots Associated to Second Order Elliptic Operators*, (with S. Hofmann), Publ. Mat. 47 (2003), no. 2, 497-515. PDF*Wavelet characterization of weighted spaces*, (with J. García-Cuerva), J. Geom. Anal. 11 (2001), no. 2, 241-264. PDF*Two-weight norm inequalities for maximal operator and fractional integrals on non-homogeneous spaces*, (with J. García-Cuerva), Indiana Univ. Math. J. 50 (2001), no. 3, 1241-1280. PDF*On the existence of principal values for the Cauchy integral on weighted Lebesgue spaces for non-doubling measures*, (with J. García-Cuerva), J. Fourier Anal. Appl. 7 (2001), no. 5, 469-487. PDF-
*Weighted inequalities and vector-valued Calderón-Zygmund operators on non-homogeneous spaces*, (with J. García-Cuerva), Publ. Mat. 44 (2000), no. 2, 613-640. PDF

**Preprints***A note on the off-diagonal Muckenhoupt-Wheeden conjecture,*(with D. Cruz-Uribe and C. Pérez). PDF*The Dirichlet problem for elliptic systems with data in Köthe function spaces*, (with D. Mitrea, I. Mitrea and M. Mitrea). PDF*Weighted Hardy spaces associated with elliptic operators. Part I: Weighted norm inequalities for conical square functions*, (with C. Prisuelos-Arribas). PDF

*Uniform Rectifiability, Carleson measure estimates, and approximation of harmonic functions*, (with S. Hofmann and S. Mayboroda). PDF*On the \(L^p\)-Poisson semigroup associated with elliptic systems*, (with D. Mitrea, I. Mitrea and M. Mitrea). PDF*Greedy Bases in variable Lebesgue spaces*, (with D. Cruz-Uribe and E. HernĂˇndez). PDF

**Links**- AFA (Análisis de Fourier y Aplicaciones). Research Project supported by MICINN (Spain).