BOOK
Analytic Capacity, the Cauchy Transform, and Non-Homogeneous Calderon-Zygmund Theory. Birkhauser (2014).
Some reviews:
In Mathematical Reviews by T.P. Hytonen.
In Zentralblatt by Dachun Yang.
In Jahresber Dtsch Math-Ver by H. von der Mosel.



SOME RESEARCH PAPERS

NON-HOMOGENEOUS HARMONIC ANALYSIS
BMO, H1, and Calderon-Zygmund operators for non doubling measures. Math. Ann. 319 (2001), 89-149. dvi
A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderon-Zygmund decomposition. Publ. Mat. 45 (2001), 163-174. dvi
The atomic space H1 for non doubling measures in terms of a maximal operator. Trans. Amer. Math. Soc. 355 (2003), 315-348. pdf (it includes some corrections and appendix).
Weighted norm inequalities for Calderon-Zygmund operators without doubling conditions. Publ. Mat. 51:2 (2007), 397-456. pdf
Strong and weak type estimates for singular integrals with respect to measures separated by AD-regular boundaries, (with V. Chousionis). Inter. Math. Res. Not. 2014(23) (2014), 6497-6522. pdf
Improved Cotlar's inequality in the context of local Tb theorems (with H. Martikainen and M. Mourgoglou). J. Funct. Anal. 274 (2018), no. 5, 1255-1275. pdf



ANALYTIC CAPACITY AND OTHER RELATED CAPACITIES
On the analytic capacity γ+. Indiana Univ. Math. J. 51 (2002), 317-343. pdf
The planar Cantor sets of zero analytic capacity and the local T(b) theorem (with J. Mateu and J. Verdera). J. Amer. Math. Soc. 16 (2003), 19-28. pdf
Painleve's problem and the semiadditivity of analytic capacity. Acta Math. 190:1 (2003), 105-149. pdf
The semiadditivity of continuous analytic capacity and the inner boundary conjecture. Amer. J. Math. 126 (2004), 523-567. pdf
Riesz transforms and harmonic Lip1 capacity in Cantor sets (with J. Mateu). Proc. London Math. Soc. 89(3) (2004), 676-696. pdf
Bilipschitz maps, analytic capacity, and the Cauchy integral. Ann. of Math. 162:3 (2005), 1241-1302. pdf
Estimate of the Cauchy integral over Ahlfors regular curves (with M. Melnikov). In "Selected Topics in Complex Analysis", Operator Theory: Advances and Applications, Vol. 158, Birkhauser Verlag, 2005, pp. 159-176. pdf
Characterization and semiadditivity of the C1 harmonic capacity (with A. Ruiz de Villa). Trans. Amer. Math. Soc. 362 (2010) 3641-3675. pdf
Calderon-Zygmund capacities and Wolff potentials on Cantor sets. J. Geom. Anal. 21(1) (2011), 195-223. pdf
Capacities associated with Calderon-Zygmund kernels (with V. Chousionis, J. Mateu, and L. Prat). Potential Anal. 38 (2013), no. 3, 913-949. pdf
Riesz transforms of non-integer homogeneity on uniformly disconnected sets (with M.C. Reguera). Trans. Amer. Math. Soc. 368 (2016), no. 10, 7045-7095. pdf
Square functions of fractional homogeneity and Wolff potentials (with V. Chousionis and L. Prat). Int. Math. Res. Notices (2016) Vol. 2016, 2295--2319. pdf
The Riesz transform of codimension smaller than one and the Wolff energy (with B. Jaye, F. Nazarov, and M.C. Reguera). Preprint (2016). To appear in Mem. Amer. Math. Soc. pdf
Analytic capacity and projections (with Alan Chang). Preprint (2017). pdf



SINGULAR INTEGRALS AND RECTIFIABILITY
Growth estimates for Cauchy integrals of measures and rectifiability. GAFA vol. 17 (2007), 605-643. ps
Uniform rectifiability, Calderon-Zygmund operators with odd kernel, and quasiorthogonality. Proc. London Math. Soc. 98(2) (2009), 393-426. pdf
On the smoothness of Holder doubling measures (with D. Preiss and T. Toro). Calc. Var. Partial Differential Equations 35(3) (2009), 339-363. pdf
Principal values for Riesz transforms and rectifiability. J. Funct. Anal., vol. 254(7) 2008, 1811-1863. pdf
Non existence of principal values of signed Riesz transforms of non integer dimension (with A. Ruiz de Villa). Indiana Univ. Math. J. 59:1 (2010), 115-130. pdf
Mass transport and uniform rectifiability. Geom. Funct. Anal. 22 (2012), no. 2, 478-527. pdf
Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs (with A. Mas). Proc. London Math. Soc. 105(1) (2012), 49-86. pdf
Variation for Riesz transforms and uniform rectifiability, (with A. Mas). J. Eur. Math. Soc. 16(11) (2014), 2267--2321. pdf
Calderon-Zygmund kernels and rectifiability in the plane (with Chousionis, Prat and Mateu). Adv. Math. 231:1 (2012), 535-568. pdf
On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1 (with Nazarov and Volberg). Acta Math. 213:2 (2014), 237-321. pdf
The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions (with Nazarov and Volberg, 2012). Publ. Mat. 58:2 (2014), 517-532. pdf
Uniform measures and uniform rectifiability. J. Lond. Math. Soc. (2) 92 (2015), no. 1, 1-18. pdf
Square functions and uniform rectifiability (with Chousionis, Garnett and Le). Trans. Amer. Math. Soc. 368 (2016), no. 9, 6063-6102. pdf
Rectifiability via a square function and Preiss' theorem (with T. Toro). Int Math Res Notices (2015), Vol. 2015, 4638-4662. pdf
Rectifiable measures, square functions involving densities, and the Cauchy transform. Mem. Amer. Math. Soc. 245 (2017), no. 1158 pdf
Lp-estimates for the variation for singular integrals on uniformly rectifiable sets (with A. Mas). Trans. Amer. Math. Soc. 369, no. 11 (2017), 8239-8275. pdf
Non-existence of reflectionless measures for the s-Riesz transform (with L. Prat). Ann. Acad. Scient. Fenn. Math., vol. 40 (2015), 957-968. pdf
Characterization of n-rectifiability in terms of Jones' square function: Part I. Calc. Var. PDE. (2015), no. 4, 3643-3665. pdf
Characterization of n-rectifiability in terms of Jones' square function: Part II (with J. Azzam). Geom. Funct. Anal. (GAFA) 25 (2015), no. 5, 1371-1412. pdf
The Riesz transform and quantitative rectifiability for general Radon measures (with D. Girela-Sarrion). Calc. Var. Partial Differential Equations 57 (2018), no. 1, Art. 16, 63 pp. pdf
Singular integrals unsuitable for the curvature method whose L2-boundedness still implies rectifiability (with P. Chunaev and J. Mateu). Preprint (2016). To appear in J. Anal. Math. pdf
The measures with an associated square function operator bounded in L2 (with B. Jaye and F. Nazarov). Preprint (2016). To appear in Adv. Math. pdf
Rectifiability of measures and the βp coefficients. Preprint (2017). To appear in Publ. Mat. pdf
Failure of L2 boundedness of gradients of single layer potentials for measures with zero low density (with J.M. Conde-Alonso and M. Mourgoglou). Preprint (2018). To appear in Math. Ann. pdf
A family of singular integral operators which control the Cauchy transform (with P. Chunaev and J. Mateu). Preprint (2018). pdf
Characterization of rectifiable measures in terms of α-numbers (with J. Azzam and T. Toro). Preprint (2018). pdf



HARMONIC MEASURE
Singular sets for harmonic measure on locally flat domains with locally finite surface measure (with J. Azzam and M. Mourgoglou). Int Math Res Notices (2017) 2017 (12): 3751-3773. pdf
Rectifiability of harmonic measure in domains with porous boundaries (with J. Azzam and M. Mourgoglou). Preprint (2015). pdf
Absolute continuity between the surface measure and harmonic measure implies rectifiability (with Hofmann, Martell, Mayboroda, and Volberg). C. R. Math. Acad. Sci. Paris 354 (2016), no. 4, 351-355. pdf
Rectifiability of harmonic measure (with Azzam, Hofmann, Martell, Mayboroda, Mourgoglou, and Volberg). Geom. Funct. Anal. (GAFA), 26(3) (2016), 703-728. pdf
Harmonic measure and Riesz transform in uniform and general domains (with M. Mourgoglou). Preprint (2015). To appear in J. Reine Ang. Math. pdf
Mutual absolute continuity of interior and exterior harmonic measure implies rectifiability (with J. Azzam and M. Mourgoglou). Comm. Pure Appl. Math. Vol. LXX (2017), 2121-2163. pdf
The one-phase problem for harmonic measure in two-sided NTA domains (with J. Azzam and M. Mourgoglou). Analysis & PDE 10-3 (2017), 559--588. pdf
On Tsirelson's theorem about triple points for harmonic measure (with A. Volberg). International Mathematics Research Notices, Vol. 2018 (2018), No. 12, pp. 3671-3683. pdf
On a two-phase problem for harmonic measure in general domains (with J. Azzam, M. Mourgoglou and A. Volberg). Preprint (2016). To appear in Amer. J. Math. pdf
Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions (with J. Garnett and M. Mourgoglou). Duke Math. J. Vol. 167 (2018), No. 8, 1473-1524. pdf
Uniform rectifiability, elliptic measure, square functions, and ε-approximability via an ACF monotonicity formula (with J. Azzam, J. Garnett and M. Mourgoglou). Preprint (2016). pdf
A two-phase free boundary problem for harmonic measure and uniform rectifiability (with J. Azzam and M. Mourgoglou). Preprint (2017). pdf
Harmonic measure and quantitative connectivity: geometric characterization of the Lp solvability of the Dirichlet problem. Part II (with J. Azzam and M. Mourgoglou). Preprint (2018). pdf



QUASICONFORMAL MAPPINGS, SOBOLEV SPACES, AND RELATED TOPICS
Analytic capacity and quasiconformal mappings with W1,2 Beltrami coefficient, (with Albert Clop). Math. Res. Lett. 15 (2008), no. 4, 779-793. pdf
Quasiconformal maps, analytic capacity, and non linear potentials (with I. Uriarte-Tuero). Duke Math. J. 162 (2013), no. 8, 1503-1566. pdf
Quasiconformal distortion of Hausdorff measures. Preprint (2009). pdf
Hausdorff measure of quasicircles (with I. Prause and I. Uriarte-Tuero). Adv. Math. 229:2 (2012), 1313-1328 pdf
Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane, (with Astala, Clop, Verdera and Uriarte-Tuero). Amer. J. Math. 135 (2013), no. 1, 17-52. pdf
Smoothness of the Beurling transform in Lipschitz domains (with V. Cruz). J. Funct. Anal. 262(10) (2012), 4423-4457. pdf
Regularity of C1 and Lipschitz domains in terms of the Beurling transform. J. Math. Pures Appl. (9) 100 (2013), no. 2, 137-165. pdf
A T(P) theorem for Sobolev spaces on domains (with M. Prats). J. Funct. Anal. 268 (2015), no. 10, 2946--2989. pdf



SURVEYS AND EXPOSITORY PAPERS
On the semiadditivity of analytic capacity and planar Cantor sets, (with J. Mateu and J. Verdera) Contemp. Math. 320 (2003), 259-278. pdf
Analytic capacity and Calderon-Zygmund theory with non doubling measures, Lecture notes of a course given at the Universidad de Sevilla in December 2003. pdf
Singularitats de funcions analitiques, integrals singulars i conjunts fractals, Butl. Soc. Catalana Mat. 17 (2002), no. 2, 75-90 (in Catalan). pdf
Painleve's poblem, analytic capacity and curvature of measures, Proceedings of the Fourth European Congress, 2004. pdf
Painleve's poblem and analytic capacity, Lecture notes of a minicourse given at El Escorial, 2004. pdf
Analytic capacity, rectifiability, and the Cauchy integral, Proceedings of the ICM 2006, Madrid. pdf
The T1 theorem. Notes of a short PhD course on the classical T1 theorem of David and Journe, given in 2012 at Barcelona and typed by V. Chousionis. pdf
About the Jones-Wolff Theorem on the Hausdorff dimension of harmonic measure (with Cuf and Verdera). Lecture Notes of a series of reading seminars held at the UAB in 2017. pdf