Harmonic analysis and its interactions with geometric measure theory and PDEs.

Google Scholar and Mathematical Reviews (ID: 1234739)

Papers
arXiv link to my papers.

[17] L^p estimates of the maximal Schrödinger operator in R^n, (with J. Li). [arXiv]

[16] L^p weighted Fourier restriction estimates, (with J. Li, H. Wang, and R. Zhang). [arXiv]

[15] Weighted refined decoupling estimates and application to Falconer distance set problem, (with Y. Ou, K. Ren, and R. Zhang). [arXiv]

[14] New improvement to Falconer distance set problem in higher dimensions, (with Y. Ou, K. Ren, and R. Zhang). [arXiv] [featured in Quanta]

[13] On a free Schrödinger solution studied by Barceló–Bennett–Carbery–Ruiz–Vilela, (with Y. Ou, H. Wang, and R. Zhang), Contemporary Mathematics. [arXiv]

[12] Weighted Fourier extension estimates and applications, Proc. Int. Cong. Math. 2022, Vol. 4, pp. 3190–3201. EMS Press, Berlin, 2023. [journal]

[11] On the multiparameter Falconer distance problem, (with Y. Ou and R. Zhang), Tran. Amer. Math. Soc. 375 (2022), no.7, 4979-5010. [arXiv][journal]

[10] An improved result for Falconer’s distance set problem in even dimensions, (with A. Iosevich, Y. Ou, H. Wang, and R. Zhang), Math. Ann. 380 (2021), no. 3-4, 1215-1231. [arXiv][journal]

[9] Counterexamples to L^p collapsing estimates, (with M. Machedon), Illinois J. Math. 65 (2021), no. 1, 191-200. [arXiv][journal]

[8] Weighted restriction estimates and application to Falconer distance set problem, (with L. Guth, Y. Ou, H. Wang, B. Wilson, and R. Zhang), Amer. J. Math. 143 (2021), no. 1, 175-211. [arXiv][journal]

[7] Recent progress on pointwise convergence for the Schrödinger equation in R^2, (with X. Li), Proceedings of the International Consortium of Chinese Mathematicians 2018, 613-626, Int. Press, Boston, MA, 2020.

[6] Lower bounds for estimates of the Schrödinger maximal function, (with J. Kim, H. Wang, and R. Zhang), Math. Res. Lett. 27 (2020), no. 3, 687-692. [arXiv][journal]

[5] Upper bounds for Fourier decay rates of fractal measures, J. Lond. Math. Soc. (2) 102 (2020), no. 3, 1318-1336. [arXiv][journal]

[4] l^p decoupling for restricted k-broadness, (with X. Li), Math. Z. 292 (2019), no. 1-2, 725-737. [arXiv][journal]

[3] Sharp L^2 estimates of the Schrödinger maximal function in higher dimensions, (with R. Zhang), Ann. of Math. (2) 189 (2019), no. 3, 837-861. [arXiv][journal]

[2] Pointwise convergence of Schrödinger solutions and multilinear refined Strichartz estimates, (with L. Guth, X. Li, and R. Zhang), Forum Math. Sigma 6 (2018), e14, 18 pp. [arXiv][journal]

[1] A sharp Schrödinger maximal estimate in R^2, (with L. Guth and X. Li), Ann. of Math. (2) 186 (2017), no. 2, 607-640. [arXiv][journal]

Others
Ph.D. Thesis

L^p estimates of maximal function related to Schrödinger equation in R^2, (with Xiaochun Li). [arXiv]