Publications

  1. A decoupling interpretation of an old argument for Vinogradov's Mean Value Theorem (with Brian Cook, Kevin Hughes, Zane Kun Li, Akshat Mudgal and Olivier Robert), submitted. [article].
  2. Sobolev spaces revisited (with Haim Brezis, Andreas Seeger and Jean Van Schaftingen), to appear in Rendiconti Lincei - Matematica e Applicazioni. [article].
  3. Spaces of Besov-Sobolev type and a problem on nonlinear approximation (with Oscar Dominguez, Andreas Seeger, Brian Street and Jean Van Schaftingen), submitted. [article].
  4. Families of functionals representing Sobolev norms (with Haim Brezis, Andreas Seeger and Jean Van Schaftingen), to appear in Analysis & PDE. [article].
  5. Bourgain-Brezis-Mironescu Convergence via Triebel-Lizorkin Spaces (with Denis Brazke and Armin Schikorra), submitted. [article].
  6. On the strict majorant property in arbitrary dimensions (with Philip T. Gressman, Shaoming Guo, Lillian B. Pierce and Joris Roos), to appear in Q. J. Math. [article].
  7. Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail (with Haim Brezis and Jean Van Schaftingen), Calc. Var. Partial Differential Equations 60 (2021), no. 4, Paper No. 129, 12pp. [article].
  8. Improved discrete restriction for the parabola (with Shaoming Guo and Zane Kun Li), to appear in Math. Res. Letts. [article].
  9. A new formula for the Lp norm (with Qingsong Gu), J. Funct. Anal. 281 (2021), no. 4, 109075. [article].
  10. Limiting Sobolev and Hardy inequalities on stratified homogeneous groups (with Jean Van Schaftingen), Ann. Fenn. Math. 47 (2022) no. 2, 1065–1098. [article].
  11. A surprising formula for Sobolev norms (with Haim Brezis and Jean Van Schaftingen), Proc. Natl. Acad. Sci. 118 (2021) no. 8, e2025254118. [article].
  12. A short proof of ℓ2 decoupling for the moment curve (with Shaoming Guo, Changkeun Oh, Joris Roos and Pavel Zorin-Kranich), Amer. J. Math. 143 (2021), no. 6, 1983-1998 [article].
  13. Decoupling for two quadratic forms in three variables: a complete characterization (with Shaoming Guo, Changkeun Oh, Joris Roos and Pavel Zorin-Kranich), to appear in Rev. Mat. Iberoam. [article].
  14. A bilinear proof of decoupling for the cubic moment curve (with Shaoming Guo and Zane Kun Li), Trans. AMS. 374 (2021), no. 8, 5405-5432. [article]
  15. Reversing a philosophy: from counting to square functions and decoupling (with Philip T. Gressman, Shaoming Guo, Lillian B. Pierce and Joris Roos), J. Geom. Anal. 31 (2021), no.7, 7075-7095 (In "Elias M. Stein: In Memoriam"). [article]
  16. Maximal functions associated with families of homogeneous curves: Lp bounds for p ≤ 2 (with Shaoming Guo, Joris Roos and Andreas Seeger), Proc. Edinb. Math. Soc. 63 (2020), no. 2, 398-412. [article]
  17. A maximal function for families of Hilbert transforms along homogeneous curves (with Shaoming Guo, Joris Roos and Andreas Seeger), Math. Ann. 377 (2020), no. 1-2, 69-114. [article]
  18. Sharp variation-norm estimates for oscillatory integrals related to Carleson's theorem (with Shaoming Guo and Joris Roos), Analysis & PDE 13 (2020), no. 5, 1457-1500. [article]
  19. Solution of the tangential Kohn Laplacian on a class of non-compact CR manifolds (with Chin-Yu Hsiao), Calc. Var. Partial Differential Equations 58 (2019), no. 2, Art. 71, 62 pp. [article]
  20. Approximation in higher-order Sobolev spaces and Hodge systems (with Pierre Bousquet, Emmanuel Russ and Yi Wang), J. Funct. Anal. 276 (2019), no. 5, 1430-1478. [article]
  21. A polynomial Carleson operator along the paraboloid (with Lillian B. Pierce), Rev. Mat. Iberoam. 35 (2019), no. 2, 339-422. [article]
  22. Polynomial Carleson operators along monomial curves in the plane (with Shaoming Guo, Lillian B. Pierce and Joris Roos), J. Geom. Anal. 27 (2017), no. 4, 2977-3012. [article]
  23. Bourgain-Brezis Estimates on Symmetric Spaces of Non-compact Type (with Sagun Chanillo and Jean Van Schaftingen), J. Funct. Anal. 273 (2017), no. 4, 1504-1547. [article]
  24. The incompressible Navier-Stokes flow in two dimensions with prescribed vorticity (with Sagun Chanillo and Jean van Schaftingen), in Sagun Chanillo, Bruno Franchi, Guozhen Lu, Carlos Perez and Eric T. Sawyer (eds.), Harmonic Analysis, Partial Differential Equations and Applications, Birkhauser, Applied and Numerical Harmonic Analysis, 2017, 19-25. [article]
  25. Variations on a proof of a borderline Bourgain-Brezis Sobolev embedding theorem (with Sagun Chanillo and Jean Van Schaftingen), Chin. Ann. Math. Ser. B 38 (2017), no. 1, 235-252. [article]
  26. On a trilinear singular integral form with determinantal kernel (with Philip T. Gressman, Danqing He, Vjekoslav Kovač, Brian Street and Christoph Thiele), Proc. Amer. Math. Soc. 144 (2016), no. 8, 3465-3477. [article]
  27. Applications of Bourgain-Brezis inequalities to Fluid Mechanics and Magnetism (with Sagun Chanillo and Jean van Schaftingen), C. R. Math. Acad. Sci. Paris, Vol. 354 (2016), no. 1, 51-55. [article]
  28. Solving the Kohn Laplacian on asymptotically flat CR manifolds of dimension 3 (with Chin-Yu Hsiao), Adv. Math. 281 (2015), 734-822. [article]
  29. A sharp subelliptic Sobolev embedding theorem with weights, Bull. London Math. Soc. 47 (2015), no. 3, 396-406. [article]
  30. Absence of Self-Similar Blow-up and Local Well-posedness for the Constant Mean-Curvature Wave Equation (with Sagun Chanillo), J. Funct. Anal. 269 (2015), no. 4, 1180-1202. [article]
  31. A subelliptic Bourgain-Brezis inequality (with Yi Wang), J. Eur. Math. Soc 16 (2014), 649-693. [article]
  32. Pseudodifferential operators of mixed type adapted to distributions of k-planes (with Elias M. Stein), Math. Res. Lett. 20 (2013), no. 6, 1183-1208. [article]
  33. The tangential Cauchy-Riemann complex on the Heisenberg group Via Conformal Invariance (with Chin-Yu Hsiao), Bulletin of the Institute of Mathematics, Academia Sinica (New Series), Vol. 8 (2013), no. 3, 359-375. [article]
  34. Wave Equations Associated to Liouville Systems and Constant Mean Curvature equations (with Sagun Chanillo), Adv. Math, Vol 235 (2013), 187-207. [article]
  35. An improved Strichartz estimate for systems with divergence free data (with Sagun Chanillo), Comm. PDE., Vol 37 (2012), no. 2, 225-233. [article]
  36. Sobolev inequality for (0,q) forms on CR manifolds of finite type, Math. Res. Lett. 17 (2010), no. 1, 177-196. [article]
  37. Doubling properties of self-similar measures, Indiana Univ. Math. J. 56 No. 2 (2007), 965-990. [article]
  38. Calculus on the Sierpinski gasket I: polynomials, exponentials and power series (with Jonathan Needleman, Robert Strichartz and Alexander Teplyaev), J. Funct. Anal. 215 (2004), 290-340. [article]