Research

My research interests are in the areas of classical harmonic analysis and its related fields. 

I've been working with multi-parameter and multilinear singular integral operators with their Banach-valued extensions, as well as Fourier restriction problems. Some key words of my research are multi-parameter T1/Tb theorems, representation theorems, dyadic shifts, iterated commutators, multi-parameter BMO spaces, time-frequency analysis, multilinear multipliers, UMD spaces, bilinear Hilbert transform, L^p theory for outer measures, sparse operator domination, weighted norm inequalities, restriction estimates, polynomial methods, etc. 

Publications:

  1. A sparse domination principle for rough singular integrals, with José M. Conde-Alonso, Amalia Culiuc, and Francesco Di Plinio, Anal. PDE, to appear (2016). arXiv
  2. Uniform sparse domination of singular integrals via dyadic shifts, with Amalia Culiuc and Francesco Di Plinio, Math. Res. Lett., to appear (2016). arXiv
  3. Little BMO and Journé commutators, with Stefanie Petermichl, Harmonic analysis, function theory, operator theory and applications, to appear (2015). preprint
  4. A modulation invariant Carleson embedding theorem outside local L^2, with Francesco Di Plinio, J. Anal. Math., to appear (2015). arXiv
  5. Banach-valued multilinear singular integrals, with Francesco Di Plinio, Indiana Univ. Math. J., to appear (2015). arXiv
  6. Higher order Journé commutators and characterizations of multi-parameter BMO, with Stefanie Petermichl and Elizabeth Strouse, Adv. Math. 291 (2016), 24-58. DOI: 10/1016/j.aim.2015.12.029. arXiv
  7. Multi-parameter singular integral operators and representation theorem, Rev. Mat. Iberoam. 33 (2017), no. 1, 325-350. DOI: 10.4171/RMI/939. arXiv
  8. Upper bound for multi-parameter iterated commutators, with Laurent Dalenc, Publ. Mat. 60 (2016), 191-220. DOI: 10.5565/PUBLMAT_60116_07. arXiv
  9. A T(b) theorem on product spaces, Trans. Amer. Math. Soc. 367 (2015), no. 9, 6159-6197. DOI: 10.1090/S0002-9947-2015-06246-1. arXiv 

Preprints:

  1. Sparse domination of Hilbert transforms along curves, with Laura Cladek, submitted (2017). arXiv
  2. A cone restriction estimate using polynomial partitioning, with Hong Wang, submitted (2017). arXiv
  3. Product BMO, little BMO and Riesz commutators in the Bessel setting, with Xuan Thinh Duong, Ji Li, Brett D. Wick, and Dongyong Yang, submitted (2016). arXiv
  4. Domination of multilinear singular integrals by positive sparse forms, with Amalia Culiuc and Francesco Di Plinio, submitted (2016). arXiv

Ph.D. dissertation: Multi-parameter commutators and new function spaces of bounded mean oscillation, Brown University (2016). pdf

Slides:

  1. Sparse domination of singular integral operators. pdf
  2. Domination of multilinear singular integrals by positive sparse forms. pdf
  3. Banach-valued T(1) type theorems. pdf
  4. Commutators of singular integrals. pdf
  5. T(1) and T(b) theorems on product spaces. pdf