## Song-Ying Li

Professor, Mathematics

School of Physical Sciences

School of Physical Sciences

Ph.D., University of Pittsburgh, 1992

University of California, Irvine

524 Rowland Hall

Mail Code: 3875

Irvine, CA 92697

524 Rowland Hall

Mail Code: 3875

Irvine, CA 92697

**Research Interests**

Complex analysis, harmonic analysis and non-linear PDEs

**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

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.

Science in China, 2009.

On Characterization for a class of pseudoconvex domains with positive constant pseudo scalar curvature on their boundaries.

CAG, 2009

CAG, 2009

On Characterizations of Isometries on Function Spaces (joint with Yingbin Ruan).

Sciences in China, 51(2008), 620--631.

Sciences in China, 51(2008), 620--631.

On Pseudo-hermitian CR Manifolds.

Proceeding of ICCM 2004, Hong-Kong}, to appear

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.

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

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.

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

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

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

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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.

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

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.

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.

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.

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.

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

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

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

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

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

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

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

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.

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.

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

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.

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.

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

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.

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.

(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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

J. of Functional Analysis, 111 (1993), pp 350-379.

Corona problem of several complex variables, Contemporary Mathematics, 137 (1992),

307–328.

307–328.

Toeplitz and Hankel operators on H p (S ) with 0 < p

1, Integral Equations and

Operator Theory, 5(1992), 807–824.

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.

5(1988), 1243–1255.

Hayman directions of meromorphic functions in the complex plane, Acta Math. Sinica

Series (2), 4(1988), 97–110.

Series (2), 4(1988), 97–110.

On normal families of meromorphic functions (with H. Xie), Acta Math. Sinica

4(1986), 468–476.

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.

Univ. 2(1986), 1–7.

Moduli distribution and normal families (with H. Xie), Pure and Appl. Math. (China)

1(1986), 57–67.

1(1986), 57–67.

On normal families of meromorphic functions (with H. Xie), Advance in Math., China

1(1985) 71–73.

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.

values, J. Fujian Normal Univ. 1(1984), 21–38.

**Professional Societies**

AMS

**Last updated**

06/15/2010