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. Birkhäuser/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),Adv. Math. 203 (2006), no. 1, 256-318. PDF
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 \(A_\infty\) weights and applications, (with D. Cruz-Uribe and C. Pérez), J. Funct. Anal. 213 (2004), 412-439. PDF
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
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. Hernández). PDF
Links
AFA
(Análisis de Fourier y Aplicaciones). Research Project supported by MICINN
(Spain).