Publications:
  • The strong geometric lemma in the Heisenberg group (with S. Li and R. Young)
    Submitted. pdf
  • The Riesz transform on intrinsic Lipschitz graphs in the Heisenberg group (with S. Li and R. Young)
    Submitted. pdf
  • The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups (with S. Li and R. Young)
    J. Reine Angew. Math. 784 (2022), 251--274. pdf
  • Porosity in conformal dynamical systems (with M. Urbanski)
    Math. Proc. Cambridge Philos. Soc. 172 (2022), no. 2, 303--371. pdf
  • Singular integrals on C^{1,a} regular curves in Carnot groups (with S. Li and S. Zimmerman)
    J. Analyse Math. (2022), no. 1, 299–326. pdf
  • On uniform measures in the Heisenberg group. (with V. Magnani and J. T. Tyson)
    Adv. Math. 363 (2020), 106980. pdf
  • Bi-Lipschitz embeddings of Heisenberg submanifolds into Euclidean spaces. (with S. Li, V. Vellis and S. Zimmerman)
    Ann. Acad. Sci. Fenn. Math. 45 (2020), no. 2, 931-955. pdf
  • On the dimension spectrum of infinite subsystems of continued fractions (with D. Leykekhman and M. Urbanski)
    Trans. Amer. Math. Soc. 373 (2020), no. 2, 1009-1042. pdf
  • Conformal Graph Directed Markov Systems on Carnot groups. (with J. T. Tyson and M. Urbanski)
    Mem. Amer. Math. Soc. 266 (2020), no. 1291, viii+155 pp. pdf
  • Boundedness of singular integrals on C^{1,a} intrinsic graphs in the Heisenberg group (with T. Orponen and K. Fassler)
    Adv. Math. 354 (2019), 106745, 45 pp. pdf
  • Intrinsic graphs and vertical beta numbers in the Heisenberg group. (with T. Orponen and K. Fassler)
    Amer. J. Math. vol. 141 no. 4, (2019), p. 1087-1147. pdf
  • The dimension spectrum of graph directed Markov systems (with D. Leykekhman and M. Urbanski)
    Selecta Math. 25 (2019), no. 3, Art. 40 pdf
  • The traveling salesman theorem on Carnot groups (with S. Li and S. Zimmerman)
    Calc. Var. PDE. 58 (2019), no. 1, Art. 14, pdf
  • Nonnegative kernels and 1-rectifiability in the Heisenberg group. (with S. Li)
    Anal. PDE 10-6 (2017), 1407-1428. pdf
  • Square Functions of Fractional Homogeneity and Wolff Potentials. (with L. Prat and X. Tolsa)
    Int. Math. Res. Not. no.9 (2016), 2295–2319. pdf
  • Some Calderón-Zygmund kernels and their relations to Wolff capacities and rectifiability. (with L. Prat)
    Math. Z. 282 (2016) no. 1-2, 435–460. pdf
  • Square functions and uniform rectifiability. (with J. Garnett, T. Le and X. Tolsa)
    Trans. Math. Amer. Soc. 368 (2016), no. 8, 6063–6102. pdf
  • Removable sets for homogeneous linear PDE in Carnot groups (with J. T. Tyson)
    J. Analyse Math. 27 (2016), 215–238. pdf
  • Marstrand's density theorem in the Heisenberg group. (with J. T. Tyson)
    Bull. Lond. Math. Soc. 47 (2015), no. 5, 771–788. pdf
  • Removable sets for Lipschitz harmonic functions on Carnot groups. (with V. Magnani and J. T. Tyson)
    Calc. Var. PDE. 3 no. 3-4 (2015) 755–780. pdf
  • Fractal solutions of dispersive PDE. (with M. B. Erdogan and N. Tzirakis)
    Proc. Lond. Math. Soc. (2015) 110 (3): 543–564. pdf
  • A note on weak convergence of singular integrals in metric spaces. (with M. Urbanski)
    Math. Res. Lett. Volume 22, No. 01, (2015) 11–21. pdf
  • Homogeneous kernels and self similar sets. (with M. Urbanski)
    Indiana Univ. Math. J. 64 No. 2 (2015), 411–431. pdf
  • Strong and weak estimates for singular integrals of measures separated by AD-regular boundaries. (with X. Tolsa)
    Int. Math. Res. Not. 23 (2014), 6497–6522. pdf
  • Singular integrals on self-similar subsets of metric groups. (with P. Mattila)
    Proc. Conf. ”Further Developments in Fractals and Related Fields”, in ”Trends in Mathematics” of Birkhauser (2014). pdf
  • Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups. (with P. Mattila)
    J. Reine Angew. Math. 691 (2014), 29–60. pdf
  • Capacities associated with Calderón-Zygmund kernels. (with J. Mateu, L. Prat and X. Tolsa)
    Potential Anal. 38 (2013), no. 3, 913–949. pdf
  • Calderón-Zygmund kernels and rectifiability in the plane. (with J. Mateu, L. Prat and X. Tolsa)
    Adv. Math. 231:1 (2012), 535-568. pdf
  • Singular integrals on Ahlfors-David regular subsets of the Heisenberg group. (with P. Mattila)
    J. Geom. Anal. 21 (2011), no. 1, 56-77.     pdf
  • Boundedness and convergence for singular integrals of measures separated by Lipschitz graphs. (with P. Mattila)
    Bull. Lond. Math. Soc. 42 (2010), no. 1, 109-118.     pdf
  • Directed porosity on conformal iterated function systems and weak convergence of singular integrals.
    Ann. Acad. Sci. Fenn. Math. 34 (2009), no. 1, 215-232.     pdf
  • Singular integrals on Sierpinski gaskets.
    Publ. Mat. 53 (2009), no. 1, 245-256.     pdf