University of Illinois at Urbana-Champaign

Xiaochun Li


Professor
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street (MC-382)
Urbana, Illinois 61801-2975
Office: 342 Illini Hall
Phone: (217) 244-2642
Fax:  (217) 333-9576
e-mail: xcli@math.uiuc.edu



Area of interest and specialization:

Harmonic Analysis

Teaching

Preprints and Papers

  1. (with X. Du L. Guth), A sharp Schrodinger maximal estimate in R^2, to appear in Annals of Math ( pdf)

  2. (with X. Du) l^p-decoupling for (k,p)-broadness, ( pdf)

  3. (with L. Xiao), Uniform estimates for bilinear Hilbert transforms and bilinear maximal functions associated to polynomials, Ameri. J. of Math, 138 (2016), No. 4, 907-962. ( pdf)

  4. (with Y. Hu), Local well-posedness of periodic fifth order KdV type equations, Journal of Geometric Analysis 25 (2015), No. 2, 709-739. ( pdf)

  5. (with Y. Hu), Discrete Fourier restriction associated with Schrodinger equations, Revista Matematica Iberoamericana 30 (2014), No. 4, 1281-1300. ( pdf)

  6. (with Y. Hu), Discrete Fourier restriction associated with KdV equations, Analysis & PDE Vol 6 (2013), No.4, 859-892. ( pdf)

  7. Bilinear Hilbert transforms along curves, I, Analysis & PDE Vol. 6 (2013), No. 1, 197-220. ( pdf)

  8. (with D. Bilyk, M. Lacey and B. Wick), Composition of Haar Paraproducts: The Random Case, Analysis Mathematica 35 (2009), No.1, 1-13. ( pdf)

  9. (with D. Fan), A bilinear oscillatory integral along parabolas, Positivity, 13 (2009), 339-366. ( Go to the paper)

  10. Uniform estimates for some paraproducts, N. Y. J. Math. 14 (2008), 145-192. ( Go to the paper)

  11. (with C. Muscalu), Generalizations of the Carleson-Hunt theorem I. The classical singularity case, Amer. J. of Math., Vol 129, No. 4. (2007), 983-1018. (pdf)

  12. (with M. Lacey), On a Stein conjecture on the Hilbert transform on vector fields, Memoirs of the AMS, to appear. (pdf)

  13. Uniform bounds for the bilinear Hilbert transform II. Revista Mat. Iberoamericana, 22, No. 3, (2006), 10679-1126. (pdf)

  14. (with M. Lacey), Maximal theorems for the directional Hilbert transform on the plane. Transactions of AMS, 358(2006), no. 9, 4099-4117. (pdf)

  15. (with M. Lacey), On a Lipschitz variant of the Kakeya maximal function, (pdf)

  16. (with L. Grafakos), The disc as a bilinear multiplier. American J. of Math., 128 (2006), 91-119. (pdf)

  17. (with M. Christ, T. Tao and C. Thiele), On multilinear osillatory integrals, singular and nonsingular. Duke Math. J., Vol. 130, No. 2, (2005), 321-351. (pdf)

  18. (with L. Grafakos), Uniform bounds for the bilinear Hilbert transforms I. Annals of Math., 159 (2004), 889-933. (pdf)

  19. (with L. Grafakos), The bilinear multiplier problem for the disc, Contemporary Math., 320 (2003), 173-193.

  20. (with S. Lu), Strongly singular convolution operators on the weighted Herz-type Hardy spaces, Acta Math. Sinica 14 (1998), 67-76.

  21. (with S. Lu and D. Yang), Some generalizations on the boundedness of bilinear operators, Approx. Theory Appl. (N. S.) 13 (1997), 8-28.

  22. (with S. Lu and D. Yang), Certain bilinear operators on Herz-type Hardy space, Beijing Mathematics 2 (1996), 75-95.

  23. Oscillatory singular integralson Hardy spaces associated with Herz spaces, Beijing Shifan Daxue Xuebao 32 (1996), 427-432.

Last modified August 21, 2017