Book
Analytic Capacity, the Cauchy Transform, and NonHomogeneous CalderonZygmund Theory. Birkhauser (2014).
Some reviews:
Some Research Papers
Nonhomogeneous harmonic analysis

BMO, H^{1}, and CalderonZygmund operators for non doubling measures. Math. Ann. 319 (2001), 89149. pdf
 A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a CalderonZygmund decomposition. Publ. Mat. 45 (2001), 163174. pdf
 The atomic space H^{1} for non doubling measures in terms of a maximal operator. Trans. Amer. Math. Soc. 355 (2003), 315348. pdf (it includes some corrections and appendix).
 Weighted norm inequalities for CalderonZygmund operators without doubling conditions. Publ. Mat. 51:2 (2007), 397456. pdf
 Strong and weak type estimates for singular integrals with respect to measures separated by ADregular boundaries, (with V. Chousionis). Inter. Math. Res. Not. 2014(23) (2014), 64976522. 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, 12551275. pdf
Analytic capacity and other related capacities
 On the analytic capacity γ_{+}. Indiana Univ. Math. J. 51 (2002), 317343. 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), 1928. pdf
 Painleve's problem and the semiadditivity of analytic capacity. Acta Math. 190:1 (2003), 105149. pdf
 The semiadditivity of continuous analytic capacity and the inner boundary conjecture. Amer. J. Math. 126 (2004), 523567. pdf
 Riesz transforms and harmonic Lip_{1} capacity in Cantor sets (with J. Mateu). Proc. London Math. Soc. 89(3) (2004), 676696. pdf
 Bilipschitz maps, analytic capacity, and the Cauchy integral. Ann. of Math. 162:3 (2005), 12411302. 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. 159176. pdf
 Characterization and semiadditivity of the C^{1} harmonic capacity (with A. Ruiz de Villa). Trans. Amer. Math. Soc. 362 (2010) 36413675. pdf
 CalderonZygmund capacities and Wolff potentials on Cantor sets. J. Geom. Anal. 21(1) (2011), 195223. pdf
 Capacities associated with CalderonZygmund kernels (with V. Chousionis, J. Mateu, and L. Prat). Potential Anal. 38 (2013), no. 3, 913949. pdf
 Riesz transforms of noninteger homogeneity on uniformly disconnected sets (with M.C. Reguera). Trans. Amer. Math. Soc. 368 (2016), no. 10, 70457095. pdf
 Square functions of fractional homogeneity and Wolff potentials (with V. Chousionis and L. Prat). Int. Math. Res. Not. IMRN (2016) Vol. 2016, 22952319. pdf
 The Riesz transform of codimension smaller than one and the Wolff energy (with B. Jaye, F. Nazarov, and M.C. Reguera). Mem. Amer. Math. Soc. 266 (2020), no. 1293.pdf
 Analytic capacity and projections (with Alan Chang). J. Eur. Math. Soc. (JEMS) 22 (2020), no. 12, 41214159. pdf
 On C^{1}approximability of functions by solutions of second order elliptic equations on plane compact sets and Canalytic capacity (with P.V. Paramonov). Anal. Math. Phys. 9 (2019), no. 3, 11331161. pdf
 Removable singularities for Lipschitz caloric functions in time varying domains (with J. Mateu and L. Prat). Preprint (2020). To appear in Rev. Mat. Iberoamericana. pdf
Singular integrals, square functions, and rectifiability
 Growth estimates for Cauchy integrals of measures and rectifiability. GAFA vol. 17 (2007), 605643. ps
 Uniform rectifiability, CalderonZygmund operators with odd kernel, and quasiorthogonality. Proc. London Math. Soc. 98(2) (2009), 393426. pdf
 On the smoothness of Holder doubling measures (with D. Preiss and T. Toro). Calc. Var. Partial Differential Equations 35(3) (2009), 339363. pdf
 Principal values for Riesz transforms and rectifiability. J. Funct. Anal., vol. 254(7) 2008, 18111863. 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), 115130. pdf
 Mass transport and uniform rectifiability. Geom. Funct. Anal. 22 (2012), no. 2, 478527. pdf
 Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs (with A. Mas). Proc. London Math. Soc. 105(1) (2012), 4986. pdf
 Variation for Riesz transforms and uniform rectifiability, (with A. Mas). J. Eur. Math. Soc. 16(11) (2014), 22672321. pdf
 CalderonZygmund kernels and rectifiability in the plane (with Chousionis, Prat and Mateu). Adv. Math. 231:1 (2012), 535568. pdf
 On the uniform rectifiability of ADregular measures with bounded Riesz transform operator: the case of codimension 1 (with Nazarov and Volberg). Acta Math. 213:2 (2014), 237321. pdf
 The Riesz transform, rectifiability, and removability for Lipschitz harmonic functions (with Nazarov and Volberg, 2012). Publ. Mat. 58:2 (2014), 517532. pdf
 Uniform measures and uniform rectifiability. J. Lond. Math. Soc. (2) 92 (2015), no. 1, 118. pdf
 Square functions and uniform rectifiability (with Chousionis, Garnett and Le). Trans. Amer. Math. Soc. 368 (2016), no. 9, 60636102. pdf
 Rectifiability via a square function and Preiss' theorem (with T. Toro). Int. Math. Res. Not. IMRN (2015), Vol. 2015, 46384662. pdf
 Rectifiable measures, square functions involving densities, and the Cauchy transform. Mem. Amer. Math. Soc. 245 (2017), no. 1158 pdf
 L^{p}estimates for the variation for singular integrals on uniformly rectifiable sets (with A. Mas). Trans. Amer. Math. Soc. 369, no. 11 (2017), 82398275. pdf
 Nonexistence of reflectionless measures for the sRiesz transform (with L. Prat). Ann. Acad. Scient. Fenn. Math., vol. 40 (2015), 957968. pdf
 Characterization of nrectifiability in terms of Jones' square function: Part I. Calc. Var. PDE. (2015), no. 4, 36433665. pdf
 Characterization of nrectifiability in terms of Jones' square function: Part II (with J. Azzam). Geom. Funct. Anal. (GAFA) 25 (2015), no. 5, 13711412. pdf
 The Riesz transform and quantitative rectifiability for general Radon measures (with D. GirelaSarrion). Calc. Var. PDE 57 (2018), no. 1, Art. 16, 63 pp. pdf
 Singular integrals unsuitable for the curvature method whose L^{2}boundedness still implies rectifiability (with P. Chunaev and J. Mateu). J. Anal. Math. 138 (2019), no.2, 741764. pdf
 The measures with an associated square function operator bounded in L^{2} (with B. Jaye and F. Nazarov). Adv. Math., 339, 1 (2018), 60112. pdf
 Rectifiability of measures and the β_{p} coefficients. Publ. Mat. 63 (2019), 491519. pdf
 Failure of L^{2} boundedness of gradients of single layer potentials for measures with zero low density (with J.M. CondeAlonso and M. Mourgoglou). Math. Ann. 373 (2019), 253285. pdf
 A family of singular integral operators which control the Cauchy transform (with P. Chunaev and J. Mateu). Math. Z. 294 (2020), 12831340. pdf
 L^{2}boundedness of gradients of single layer potentials and uniform rectifiability (with L. Prat and C. Puliatti). Preprint (2018). To appear in Analysis & PDE. pdf
 Characterization of rectifiable measures in terms of αnumbers (with J. Azzam and T. Toro). Trans. Amer. Math. Soc. 373 (2020), no. 11, 79918037. pdf
 Jump formulas for singular integrals and layer potentials on rectifiable sets. Proc. Amer. Math. Soc. 148(11) (2020), 47554767. pdf
 A proof of Carleson's ε^{2}conjecture (with B. Jaye and M. Villa). Ann. of Math. (2) 194 (2021), no. 1, 97161.
pdf
 The measures with L^{2}bounded Riesz transform satisfying a subcritical Wolfftype energy condition (with Damian Dąbrowski). Preprint (2021).
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 The measures with L^{2}bounded Riesz transform and the Painlevé problem for Lipschitz harmonic functions. Preprint (2021).
pdf
Harmonic measure, unique continuation, and related topics
 Singular sets for harmonic measure on locally flat domains with locally finite surface measure (with J. Azzam and M. Mourgoglou). Int. Math. Res. Not. IMRN 2017(12) (2017), 37513773. 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, 351355. pdf
 Rectifiability of harmonic measure (with Azzam, Hofmann, Martell, Mayboroda, Mourgoglou, and Volberg). Geom. Funct. Anal. (GAFA), 26(3) (2016), 703728. pdf
 Harmonic measure and Riesz transform in uniform and general domains (with M. Mourgoglou). J. Reine Angew. Math. 758 (2020), 183221. 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), 21212163. pdf
 The onephase problem for harmonic measure in twosided NTA domains (with J. Azzam and M. Mourgoglou). Analysis & PDE 10:3 (2017), 559588. pdf
 On Tsirelson's theorem about triple points for harmonic measure (with A. Volberg). Int. Math. Res. Not. IMRN, Vol. 2018 (2018), No. 12, pp. 36713683. pdf
 On a twophase problem for harmonic measure in general domains (with J. Azzam, M. Mourgoglou and A. Volberg). Amer. J. Math. 141(5) (2019), 12591279. pdf
 Uniform rectifiability from Carleson measure estimates and εapproximability of bounded harmonic functions (with J. Garnett and M. Mourgoglou). Duke Math. J. Vol. 167 (2018), No. 8, 14731524. pdf
 Uniform rectifiability, elliptic measure, square functions, and εapproximability via an ACF monotonicity formula (with J. Azzam, J. Garnett and M. Mourgoglou). Preprint (2016). To appear in Int. Math. Res. Not. IMRN. pdf
 A twophase free boundary problem for harmonic measure and uniform rectifiability (with J. Azzam and M. Mourgoglou). Trans. Amer. Math. Soc., vol. 373, no. 6, 2020, 43594388. pdf
 Harmonic measure and quantitative connectivity: geometric characterization of the L^{p}solvability of the Dirichlet problem (with Part I by Hofmann and Martell, and Part II by Azzam, Mourgoglou, and Tolsa). Invent. Math. 222 (2020), no. 3, 881993. pdf
 The mutual singularity of harmonic measure and Hausdorff measure of codimension smaller than one. Int. Math. Res. Not. IMRN. Vol. 2021, No. 18, pp. 1378313811
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 The twophase problem for harmonic measure in VMO (with M. Prats). Calc. Var. PDE. (2020) 59:102. pdf,
web
 Unique continuation at the boundary for harmonic functions in C^{1} domains and Lipschitz domains with small constant. Preprint (2020). To appear in Comm. Pure Appl. Math. pdf
 The regularity problem for the Laplace equation in rough domains (with M. Mourgoglou). Preprint (2021). pdf
Quasiconformal mappings, Sobolev spaces, and related topics
 Analytic capacity and quasiconformal mappings with W^{1,2} Beltrami coefficient (with Albert Clop). Math. Res. Lett. 15 (2008), no. 4, 779793. pdf
 Quasiconformal maps, analytic capacity, and non linear potentials (with I. UriarteTuero). Duke Math. J. 162 (2013), no. 8, 15031566. pdf
 Quasiconformal distortion of Hausdorff measures. Preprint (2009). pdf
 Hausdorff measure of quasicircles (with I. Prause and I. UriarteTuero). Adv. Math. 229:2 (2012), 13131328 pdf
 Quasiconformal distortion of Riesz capacities and Hausdorff measures in the plane, (with Astala, Clop, Verdera and UriarteTuero). Amer. J. Math. 135 (2013), no. 1, 1752. pdf
 Smoothness of the Beurling transform in Lipschitz domains (with V. Cruz). J. Funct. Anal. 262(10) (2012), 44234457. pdf
 Regularity of C^{1} and Lipschitz domains in terms of the Beurling transform. J. Math. Pures Appl. (9) 100 (2013), no. 2, 137165. pdf
 A T(P) theorem for Sobolev spaces on domains (with M. Prats). J. Funct. Anal. 268 (2015), no. 10, 29462989. 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), 259278. pdf
 Analytic capacity and CalderonZygmund 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, 7590 (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 JonesWolff Theorem on the Hausdorff dimension of harmonic measure (with Cufí and Verdera). Lecture Notes of a series of reading seminars held at the UAB in 2017. pdf