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.
- 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
- Uniform sparse domination of singular integrals via dyadic shifts, with Amalia Culiuc and Francesco Di Plinio, Math. Res. Lett., to appear (2016). arXiv
- Little BMO and Journé commutators, with Stefanie Petermichl, Harmonic analysis, function theory, operator theory and applications, to appear (2015). preprint
- A modulation invariant Carleson embedding theorem outside local L^2, with Francesco Di Plinio, J. Anal. Math., to appear (2015). arXiv
- Banach-valued multilinear singular integrals, with Francesco Di Plinio, Indiana Univ. Math. J., to appear (2015). arXiv
- 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
- Multi-parameter singular integral operators and representation theorem, Rev. Mat. Iberoam. 33 (2017), no. 1, 325-350. DOI: 10.4171/RMI/939. arXiv
- Upper bound for multi-parameter iterated commutators, with Laurent Dalenc, Publ. Mat. 60 (2016), 191-220. DOI: 10.5565/PUBLMAT_60116_07. arXiv
- 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
- Sparse domination of Hilbert transforms along curves, with Laura Cladek, submitted (2017). arXiv
- A cone restriction estimate using polynomial partitioning, with Hong Wang, submitted (2017). arXiv
- 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
- 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