D. Faraco, M.Prats. Characterization for stability in planar conductivities, to appear in Journal of differential equations. pdf
D. Faraco, M.Prats. Characterization for stability in planar conductivities, to appear in Journal of differential equations. pdf
M. Oliva, M.Prats. Sharp bounds for composition with quasiconformal mappings in Sobolev spaces, Journal of Mathematical Analysis and Applications (2017), 451(2), 1026–1044. pdf
M.Prats. Beltrami equations in the plane and Sobolev regularity , Communications on Pure and Applied Analysis (2018), 17(2), 319–332. pdf
M.Prats, E. Saksman. A T(1) theorem for fractional Sobolev spaces on domains , Journal of Geometric Analysis (2017), 27(3), 2490–2538. pdf
M.Prats. Sobolev regularity of quasiconformal mappings on domains , to appear in Journal d’Analyse Mathematique. pdf
M.Prats. Sobolev regularity of the Beurling transform on planar domains , Publicacions Matemàtiques (2017), 61, 291-336. pdf
A. Mas and X. Tolsa. “Lp-estimates for the variation for singular integrals on uniformly rectifiable sets”. Preprint (2015). To appear in Trans. Amer. Math. Soc. pdf
J. Azzam, M. Mourgoglou and X. Tolsa. “The one-phase problem for harmonic measure in two-sided NTA domains”. Preprint (2016). pdf
J. Azzam, M. Mourgoglou and X. Tolsa. “Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability”. Preprint (2016). To appear in Comm. Pure Appl. Math. pdf
D. Girela-Sarrion and X. Tolsa. “The Riesz transform and quantitative rectifiability for general Radon measures”. Preprint (2016). pdf
B. Jaye, F. Nazarov, M.C. Reguera and X. Tolsa. “The Riesz transform of codimension smaller than one and the Wolff energy”. Preprint (2016). pdf
J. Azzam, S. Hofmann, J.M. Martell, S. Mayboroda, M. Mourgoglou, X. Tolsa, and A. Volberg. “Rectifiability of harmonic measure”. Preprint (2015). To appear in Geom. Funct. Anal. pdf
M. Mourgoglou and X. Tolsa. “Harmonic measure and Riesz transform in uniform and general domains”. Preprint (2015). pdf
H. Martikainen, M. Mourgoglou and X. Tolsa. “Improved Cotlar’s inequality in the context of local Tb theorems”. Preprint (2015). pdf
J. Azzam, Subsets of absolute continuity for harmonic measure in NTA domains. Preprint (2015). pdf
J. Azzam, M. Mourgoglou, A characterisation of 1-rectifiable doubling measures with connected supports. Preprint (2015). pdf
J. Azzam, X. Tolsa. Characterization of n-rectifiability in terms of Jones’ square function: Part II. Preprint (2015). pdf
X. Tolsa. Characterization of n-rectifiability in terms of Jones’ square function: Part I. Preprint (2015). pdf
J. Azzam, M. Mourgoglou, X. Tolsa. Singular sets for harmonic measure on locally flat domains with locally finite boundaries. Preprint (2015). pdf
X. Tolsa. Rectifiable measures, square functions involving densities, and the Cauchy transform. Preprint (2014). pdf
V. Chousionis, L. Prat, X. Tolsa. Square functions of fractional homogeneity and Wolff potentials. Preprint (2014). pdf
M.Prats, X. Tolsa. A T(P) theorem for Sobolev spaces on domains , J. Funct. Anal. (2015), 268(10), 2946–2989. pdf
M. C. Reguera and X. Tolsa. Riesz transforms of non-integer homogeneity on uniformly disconnected sets. Preprint (2014). To appear in Trans. Amer. Math. Soc. pdf
X. Tolsa and T. Toro. Rectifiability via a square function and Preiss’ theorem. Preprint (2014). To appear in IMRN. pdf
V. Chousionis, J. Garnett, T. Le and X. Tolsa. Square functions and uniform rectifiability. Preprint (2014). To appear in Trans. Amer. Math. Soc. pdf
X. Cabré, M. Sanchón and J. Spruck. A priori estimates for semistable solutions of semilinear elliptic equations. Preprint arXiv:1407.0243 (2013). pdf.
D. Castorina and M. Sanchón. Regularity of stable solutions to semilinear elliptic equations on Riemannian models. Preprint arXiv:1312.5866 (2013). pdf.
A. Aleman, S. Pott and M.C. Reguera. Sarason Conjecture on the Bergman space, Preprint (2013). Submitted. pdf
D. Castorina and M. Sanchón. Regularity of stable solutions of p-Laplace equations through geometric Sobolev type inequalities. Preprint arXiv:1201.3486v1 (2012). pdf. To appear in JEMS
X. Tolsa. Uniform measures and uniform rectifiability, Preprint (2013). pdf
F. Nazarov, X. Tolsa and A. Volberg. The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions, Publ. Mat. 58:2 (2014), 517-532. pdf
F. Nazarov, X. Tolsa and A. Volberg. On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1. Acta Mathematica 213(2) (2014), 237-321pdf
Martí Prats, A T(1) theorem for Sobolev spaces on domains, Seminari d’Anàlisi UB-UAB, Barcelona, October 2013 (50′ talk) pdf
Martí Prats, A T(1) theorem for Sobolev spaces on domains, II Congreso de Jóvenes Investigadores, Sevilla, September 2013 (25′ talk). pdf
N. Arrizabalaga, A. Mas and L. Vega. Shell interactions for Dirac operators, submitted (2013). pdf
A. Mas. Variational inequalities for singular integral operators, Journees equations aux
derivees partielles (2012), Exp. No. 7, 14 pages, http://www.cedram.org. pdf
A. Mas. Variation for singular integrals on Lipschitz graphs: Lp and endpoint estimates, to appear in Trans. Amer. Math. Soc. (2013), 21 pages. pdf
A. Mas and X. Tolsa. Variation for the Riesz transform and uniform recti ability, J. Eur. Math. Soc. 16(11) (2014), 2267–2321. pdf
A. Mas. Failure of rational approximation on some Cantor type sets, Proc. Amer. Math. Soc., 137(2) (2009), 635-640. pdf
Martí Prats, Rectifiable Sets and the Traveling Salesman Problem, SUMMER SCHOOL T(1) and T(b) theorems and applications, Bonn, July 2013 (2h talk). pdf
M. Sanchón. W1,q estimates for the extremal solution of reaction-diffusion problems. Nonlinear Anal. 80 (2013), 49-54. pdf.
Martí Prats, Smoothness of the Beurling transform in Lipschitz domains, Doc-Course Complex Analysis and Related Areas, Málaga, March 2013 (25′ talk). pdf
X. Tolsa. Regularity of C1 and Lipschitz domains in terms of the Beurling transform, J. Math. Pures Appl. (9) 100 (2013), no. 2, 137-165. pdf
X. Cabré and M. Sanchón. Geometric-type Sobolev inequalities and applications to the regularity of minimizers. J. Funct. Anal. 264 (2013), 303-325.pdf.
V. Chousionis and X. Tolsa. Strong and weak type estimates for singular integrals with respect to measures separated by AD-regular boundaries, IMRN Vol. 2014(23) (2014), 6497-6522 . pdf
X. Tolsa. Mass transport and uniform rectifiability, Geom. Funct. Anal. 22 (2012), no. 2, 478-527. pdf
A. Mas and X. Tolsa. Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs, Proc. London Math. Soc. 105(1) (2012), 49-86. pdf
A. Mas, M. Melnikov, and X. Tolsa. A dual characterization of the C1 harmonic capacity and applications, Duke Math. J., 153(1) (2010), 1-22. pdf
See also Erratum to: “A dual characterization of the C1 harmonic capacity and applications”, Duke Math. J. 153(1) (2010), 1-22, Duke Math. J., 157(2) (2011), 421-423. pdf
X. Tolsa. Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonality, Proc. London Math. Soc. 98(2) (2009), 393-426. pdf
X. Cabré, A. Capella and M. Sanchón. Regularity of radial minimizers of reaction equations involving the p-Laplacian. Calc. Var. and PDE’s 34 (2009), 475-494.
M. Sanchón and J.M. Urbano. Entropy solutions for the p(x)-Laplace equation. Trans. Amer. Math. Soc. 361 (2009), 6387-6405.
J.F. Rodrigues, M. Sanchón and J.M. Urbano. The obstacle problem for nonlinear elliptic equations with variable growth and L1 data. Monatsh. Math 154 (2008), 303-322.
M. Sanchón. Regularity of the extremal solution of some nonlinear elliptic problems involving the p-Laplacian. Potential Anal. 27 (2007), 217- 224.
M. Sanchón. Boundedness of the extremal solution of some p-Laplacian problems. Nonlinear Anal. 67 (2007), 281-294.
X. Cabré and M. Sanchón. Stable and extremal solutions of some semilinear problems involving the p-Laplacian. Comm. Pure Appl. Anal. 6 (2007), n. 1, 43-67.
B. Abdellaoui, E. Colorado and M. Sanchón. Regularity of entropy solutions of quasilinear elliptic problems related with Hardy-Sobolev inequalities. Adv. Nonlinear Stud. 6 (2006), 547-562.
X. Cabré, M. Lucia and M. Sanchón. A mean field equation on a torus: one-dimensional symmetry of solutions. Comm. Partial Differential Equations 30 (2005), 1315-1330.
À. Calsina and M. Sanchón. Stability and instability of equilibria of an equation of size structured population dynamics. J. Math. Anal. Appl. 286 (2003), 435-452.
X. Tolsa. BMO, H1, and Calderon-Zygmund operators for non doubling measures, Math. Ann. 319 (2001), 89-149. pdf
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