Xiaochun Li
Professor
Department of Mathematics
University of Illinois at UrbanaChampaign
1409 W. Green Street (MC382)
Urbana, Illinois 618012975
Office: 342 Illini Hall
Phone: (217) 2442642
Fax: (217) 3339576
email: xcli@math.uiuc.edu
Area of interest and specialization:
Harmonic Analysis
Teaching
 Spring 2021

Math 444: Elementary Real analysis
Preprints and Papers

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

(with
X. Du)
l^pdecoupling for (k,p)broadness,
( pdf)

(with
L. Xiao),
Uniform estimates for bilinear Hilbert transforms and bilinear maximal functions
associated to polynomials,
Ameri. J. of Math, 138 (2016), No. 4, 907962.
( pdf)

(with
Y. Hu),
Local wellposedness of periodic fifth order KdV type equations,
Journal of Geometric Analysis 25 (2015), No. 2, 709739.
( pdf)

(with
Y. Hu),
Discrete Fourier restriction associated with Schrodinger equations,
Revista Matematica Iberoamericana 30 (2014), No. 4, 12811300.
( pdf)

(with
Y. Hu),
Discrete Fourier restriction associated with KdV equations,
Analysis & PDE Vol 6 (2013), No.4, 859892.
( pdf)
 Bilinear Hilbert transforms along curves, I,
Analysis & PDE Vol. 6 (2013), No. 1, 197220.
( pdf)

(with
D. Bilyk,
M. Lacey and
B. Wick),
Composition of Haar Paraproducts: The Random Case,
Analysis Mathematica 35 (2009), No.1, 113.
( pdf)
 (with
D. Fan), A bilinear oscillatory integral along parabolas,
Positivity, 13 (2009), 339366.
( Go to the paper)
 Uniform estimates for some paraproducts, N. Y. J. Math. 14 (2008), 145192.
( Go to the paper)
 (with
C. Muscalu), Generalizations of the CarlesonHunt
theorem I. The classical singularity case,
Amer. J. of Math., Vol 129, No. 4. (2007), 9831018.
(pdf)
 (with M. Lacey),
On a Stein conjecture on the Hilbert transform on vector fields,
Memoirs of the AMS, to appear.
(pdf)
 Uniform bounds for the bilinear Hilbert transform II.
Revista Mat. Iberoamericana, 22, No. 3, (2006), 106791126.
(pdf)
 (with M. Lacey),
Maximal theorems for the directional Hilbert
transform on the plane.
Transactions of AMS, 358(2006), no. 9, 40994117.
(pdf)
 (with M. Lacey),
On a Lipschitz variant of the Kakeya maximal function,
(pdf)
 (with
L. Grafakos),
The disc as a bilinear multiplier.
American J. of Math., 128 (2006), 91119.
(pdf)
 (with
M. Christ,
T. Tao and
C. Thiele), On multilinear osillatory
integrals, singular and nonsingular.
Duke Math. J., Vol. 130, No. 2, (2005), 321351.
(pdf)
 (with
L. Grafakos),
Uniform bounds for the bilinear Hilbert
transforms I.
Annals of Math., 159 (2004), 889933.
(pdf)
 (with
L. Grafakos),
The bilinear multiplier problem for the disc,
Contemporary Math., 320 (2003), 173193.
 (with
S. Lu), Strongly singular convolution operators on the weighted Herztype
Hardy spaces,
Acta Math. Sinica 14 (1998), 6776.
 (with
S. Lu and
D. Yang),
Some generalizations on the boundedness of bilinear
operators,
Approx. Theory Appl. (N. S.) 13 (1997), 828.
 (with
S. Lu and
D. Yang),
Certain bilinear operators on Herztype Hardy space,
Beijing Mathematics 2 (1996), 7595.
 Oscillatory singular integralson Hardy spaces associated with Herz spaces,
Beijing Shifan Daxue Xuebao 32 (1996), 427432.
Last modified August 21, 2017