SongYing LiProfessor, Mathematics 
Research Interests 
Complex analysis, harmonic analysis and nonlinear PDEs  
URL  www.math.uci.edu/~sli/  
Academic Distinctions  ISSAC Award, Japan (1999). Faculty Career Development Award, UC Irvine (1996). Andrew Mellon Predoctoral Fellowship (19881990). Natural Science Prize of Fujian Provinces, China (1988).  
Appointments 
July1, 2004present: Professor, Department of Mathematics, UCI; 20002004: Associate Professor, Department of Mathematics, UC Irvine. 19962000: Assistant Professor, Department of Mathematics, UC Irvine. 19941996: 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), 620631. 

On Pseudohermitian CR Manifolds. Proceeding of ICCM 2004, HongKong}, to appear 

On proper harmonic map between two strictly pseudoconvex domains with K\"ahler metrics (with E. Simon), Asian Journal of Mathematics, 11(2007), 251276. 

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 pseudohermitian manifold and its application to torsionfree hypersurfaces (with HS. 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), 673701 

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), 477491 

Characterization for Balls by Potential Function of KahlerEinstein Metrics for domains in C^n. Comm. in Analysis and Geometry,} 13(2005), 461478. 

Some function theoretical results on domains in Cn , Proceeding of ICCM 2001, Editors: CS 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 MongeAmp`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 SubLaplacian on a PseudoHermitian Manifolds (with HS. Luk), Proc. AMS, 132(2003), 789798 

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 subLaplacian on the boundary of the unit sphere in Cn (with DC. 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 MongeAmp`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), 333354 

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 MongeAmp`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 Pseudohermitian CR Manifolds. Proceeding of ICCM 2004, HongKong, to appear. 

On proper harmonic map between two strictly pseudoconvex domains with K\"ahler metrics (with E. Simon), Asian Journal of Mathematics, 11(2007), 251276. 

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 pseudohermitian manifold and its application to torsionfree hypersurfaces (with HS. 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), 673701 

Characterization for Balls by Potential Function of K¨ahlerEinstein Metrics for domains in C^n. Comm. in Analysis and Geometry, 13(2005), 461–478 

Characterization for Balls by Potential Function of K¨ahlerEinstein 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 MongeAmp`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), 373399. 

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 12991323. 

(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 13051327. 

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 MongeAmp`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), 5172. 

On the DunfordPettis 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 350379. 

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 

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Last updated  06/15/2010  