Song-Ying Li

Professor, Mathematics
School of Physical Sciences

Ph.D., University of Pittsburgh, 1992

Phone: (949) 824-3218
Fax: (949) 824-7993
Email: sli@math.uci.edu

University of California, Irvine
524 Rowland Hall
Mail Code: 3875
Irvine, CA 92697


Research
Interests
Complex analysis, harmonic analysis and non-linear PDEs
   
URL www.math.uci.edu/~sli/
   
Academic
Distinctions
ISSAC Award, Japan (1999). Faculty Career Development Award, UC Irvine (1996). Andrew Mellon Predoctoral Fellowship (1988-1990). Natural Science Prize of Fujian Provinces, China (1988).
   
Appointments July1, 2004--present: Professor, Department of Mathematics, UCI;
2000-2004: Associate Professor, Department of Mathematics, UC Irvine.
1996-2000: Assistant Professor, Department of Mathematics, UC Irvine.
1994-1996: Visiting Assistant Professor, Department of Mathematics, Washington University, St. Louis.t
   
Publications Compact composition operators on $BMOA(B_n)$ (with Sujuan Long).
Science in China, 2009.
   
  On Characterization for a class of pseudoconvex domains with positive constant pseudo scalar curvature on their boundaries.
CAG, 2009
   
  On Characterizations of Isometries on Function Spaces (joint with Yingbin Ruan).
Sciences in China, 51(2008), 620--631.
   
  On Pseudo-hermitian CR Manifolds.
Proceeding of ICCM 2004, Hong-Kong}, to appear
   
  On proper harmonic map between two strictly pseudoconvex domains
with K\"ahler metrics (with E. Simon),
Asian Journal of Mathematics, 11(2007), 251--276.
   
  Composition Operators and Isometries on Holomorphic Function Spaces over Domains
in Cn , The Proceedings of the International Conference on Complex Geometry and Related
Fields, AMS/IP Studies in Advanced Math., IP press, 39(2007), 161–174
   
  An explicit formula for the Webster torsion of a pseudo-hermitian manifold and its
application to torsion-free hypersurfaces (with H-S. Luk), Science in China, 49(2006),
1662–1682.
   
  An explicit formula Webster pseudo Ricci curvature and its applications for character-
izing balls in Cn+1 (with H.-S. Luk), Communication in Analysis and Geometry, 14(2006),
673-701
   
  Analysis on Besov spaces II: Embedding and Duality Theorems (with W. Luo), J. of
Math. Analysis and Applications, 333 (2007), no. 2, 1189–1202
   
  On characterization of Besov space and application. Part I (with W. Luo).
J. of Math. Analysis and Applications, 310(2005), 477-491
   
  Characterization for Balls by Potential Function of Kahler-Einstein Metrics
for domains in C^n.
Comm. in Analysis and Geometry,} 13(2005), 461--478.
   
  Some function theoretical results on domains in Cn , Proceeding of ICCM 2001, Editors:
C-S Lin, L. Yang and S.T. Yau, International press, 2004
   
  Criteria for Schatten Class Composition Operators on Hardy and Bergman Spaces,
Geometric Function Theory in Several Complex Variables, edited by Carl H FitzGerald
& Sheng Gong, 2004
   
  On the Dirichlet problems for the elementary symmetric function equations of the
eigenvalues of complex hessian.
Asian Journal of Mathematics, 8(2004), 87–106
   
  On existence and regularity for the Dirichlet boundary value problem for complex
Monge-Amp`ere equations on weakly pseudoconvex domains in C^n.
Calculus of Variation and PDEs, 20(2004), 119–132
   
  The Sharp Lower Bound for the First Positive Eigenvalue of Sub-Laplacian on a
Pseudo-Hermitian Manifolds (with H-S. Luk), Proc. AMS, 132(2003), 789-798
   
  Boundary behavior of harmonic functions of Bergman metric on polydisc (with E. Simon)
Amer. J. of Math., 124(2002), 1045–1057
   
  A Riemann zeta functions associated to sub-Laplacian on the boundary of the unit
sphere in Cn (with D-C. Chang).
Journal d’Analyse Mathematique, 86(2002), 25–48
   
  Boundedness and compactness of integral operators on space of homogeneous type
and application (II) (with S. Krantz).
J. of Math. Analysis and Applications, 258(2001),
642–657
   
  Boundedness and compactness of integral operators on space of homogeneous type
and application (I) (with S. Krantz).
J. of Math. Analysis and Applications, 258(2001), 629–641.
   
  On the Existence of Smooth Plurisubharmonic Solutions for Certain Degenerate
Monge-Amp`ere Equations (with S. Krantz), Complex variables, 41(2000), 207–219
   
  Applications of the singular integral operators in real and complex analysis, Advance
in Math. , China, 29 (2000), 481–501
   
  On the holomorphicity of proper harmonic maps between balls in Cn with Bergman
metrics (with L. Ni), Math. Ann., 316 (2000), 333-354
   
  On the Boundedness of Multipliers, Commutators and Second Derivatives of Green’s
Operators on H 1 and BM O (with D. C. Chang), Annali del la Scuola Normale Superiore
di Pisa, XX VIII (1999), 341–356
   
  On oblique boundary value problems of Monge-Amp`ere equations.
Paci?c J. of Math., 190(1999), 155–172
   
  Hankel operators in Dixmier class (with B.Russo),
C.R. Acad. Sci. Paris, t. 324, Series 1 (1997), 21–26.
   
  On some analysis of function spaces associated with Hankel operators (with S. Krantz
and R. Rochberg).
Ill. J. of Math., 41(1997), 398–411
   
  On the holomorphic extension of maps from the boundaries of K¨ahler manifolds (with J. Chen).
Tohiku Math. J., 49(1997), 585–597.
   
  Composition operators belongs to trace ideals on weighted Bergman spaces of bounded
symmetric domains in Cn (with B. Russo). Annali D. Math. Pure Appl., CLXXII,1997,
379–394.
   
  On Pseudo-hermitian CR Manifolds.
Proceeding of ICCM 2004, Hong-Kong, to appear.
   
  On proper harmonic map between two strictly pseudoconvex domains
with K\"ahler metrics (with E. Simon),
Asian Journal of Mathematics, 11(2007), 251--276.
   
  On proper harmonic map between two strictly pseudoconvex domains with Kahler
metrics (with E. Simon), Asian Journal of Mathematics, 11(2007), 251–276
   
  An explicit formula for the Webster torsion of a pseudo-hermitian manifold and its
application to torsion-free hypersurfaces (with H-S. Luk).
Science in China, 49(2006), 1662–1682
   
  An explicit formula Webster pseudo Ricci curvature and its applications for character-
izing balls in C^{n+1} (with H.-S. Luk). Communication in Analysis and Geometry, 14(2006), 673-701
   
  Characterization for Balls by Potential Function of K¨ahler-Einstein Metrics for domains in C^n.
Comm. in Analysis and Geometry, 13(2005), 461–478
   
  Characterization for Balls by Potential Function of K¨ahler-Einstein
Metrics for domains in C^n.
Comm. in Analysis and Geometry, 13(2005), 461–478
   
  On the Boundedness of Multipliers, Commutators and Second Derivatives of Green’s
Operators on H 1 and BM O (with D. C. Chang).
Annali del la Scuola Normale Superiore di Pisa, XX VIII (1999), 341–356
   
  On oblique boundary value problems of Monge-Amp`ere equations.
Pacific J. of Math., 190(1999), 155–172
   
  Effect of the boundary geometry on the Hankel operators belonging to trace ideals of
Bergman spaces, (with Krantz and Rochberg). IEOT, 28(1997), 196–213.
   
  On the real analytic hypoellipticity for dbar and dbar_b (with M. Christ).
Math. Z., 32(1997), 373-399.
   
  Area integral characterizations of functions in Hardy space on domains in C^n (with
S. Krantz), Complex variables, 32(1997), 373–399
   
  Effect of the boundary regularity on the singular numbers of the Friechers operators on
Bergman spaces, (with S. Krantz, P. Lin and R. Rochberg).
Michigan Math. J., 43(1996), 337–348.
   
  Factorization theorems for functions in subspaces of L^1 and application to Corona
problem, (with S. Krantz).
Indiana U. J. of Math., 45 (1996), 83–102.
   
  The explicit solution for the Lipschitz Corona problem in the polydisc (with S. G. Krantz).
Pacific J. of Math., vol iii (1996), 287–302
   
  Characterization of the boundedness for a family of commutators on L^p.
Col loquium Math., Vol LXX(1996), 59–71.
   
  Hadamard products for the spaces of holomorphic functions in the unit ball in C^n
(with J. Burbea), Pacific J. of Mathematics, 168(1995), 235–270.
   
  A criteria for composition operators belonging to Schatten trace ideal on Bergman spaces.
Amer. J. of Math., 117 (1995), pp 1299-1323.
   
  (with S. Krantz) "Duality theorems for Hardy and Bergman spaces on convex domain
of finite type in Cn". Ann. of the Fourier Institute in Grenoble, 45 (1995), pp 1305-1327.
   
  On the trace ideals of operators of Hankel type in a domain in Cn (with F. Beatrous),
Il linois J. of Mathematics, 39(1995), 723–754.
   
  A criteria for composition operators belonging to Schatten trace ideal on Bergman
spaces, Amer. J. of Math., 117(1995), 1299–1323.
   
  On the Neumann problems of complex Monge-Amp`ere equations, Indiana University
J. of Mathematics, 44(1995), 1099–1122.
   
  Some remarks on the Corona problem in strongly pseudoconvex domains in Cn (with
S. G. Krantz), Il lionis J. of Mathematics, 39(1995), 323–349.
   
  On the compactness of composition operators on Hardy spaces in strongly pseudo-
convex domains in Cn (with B. Russo), Proceeding of A.M.S., 123(1995), 161–172.
   
  A note on Hardy spaces and functions of bounded mean oscillation on domain in C (with S. G. Krantz).
Michigan J. of Mathematics, 41(1994), 51-72.
   
  On the Dunford-Pettis property for some functions algebras in domains in Cn (with
B. Russo), J. of London Mathematics Society, 50(1994), 392–403.
   
  On the boundedness and compactness of operators of Hankel type (with F. Beatrous) .
J. of Functional Analysis, 111 (1993), pp 350-379.
   
  Corona problem of several complex variables, Contemporary Mathematics, 137 (1992),
307–328.
   
  Toeplitz and Hankel operators on H p (S ) with 0 < p
1, Integral Equations and
Operator Theory, 5(1992), 807–824.
   
  A Plessner decomposition along transverse curves (with F. Beatrous), Can. J. Math.
5(1988), 1243–1255.
   
  Hayman directions of meromorphic functions in the complex plane, Acta Math. Sinica
Series (2), 4(1988), 97–110.
   
  On normal families of meromorphic functions (with H. Xie), Acta Math. Sinica
4(1986), 468–476.
   
  A note on Bloch law, J. Math. Res. Expo. 2(1986), 10–11.
   
  On the distributions of the singular directions of gap entire functions, J. Fujian Normal
Univ. 2(1986), 1–7.
   
  Moduli distribution and normal families (with H. Xie), Pure and Appl. Math. (China)
1(1986), 57–67.
   
  On normal families of meromorphic functions (with H. Xie), Advance in Math., China
1(1985) 71–73.
   
  On a normal criteria of a class of functions, J. Fujian Normal Univ. 1(1984), 153–158.
   
  On normal families and singular directions of meromorphic functions with multiplicity
values, J. Fujian Normal Univ. 1(1984), 21–38.
   
Professional
Society
AMS
   
   
Link to this profile http://www.faculty.uci.edu/profile.cfm?faculty_id=4833
   
Last updated 06/15/2010