Song-Ying LiProfessor, Mathematics |
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Research Interests |
Complex analysis, harmonic analysis and non-linear PDEs | |
| URL | www.math.uci.edu/faculty/sli.html | |
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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 |
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| Publications |
Compact composition operators on $BMOA(B_n)$ (with Sujuan Long). Science in China, 2009. |
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On Characterization for a class of pseudoconvex domains with positive constant pseudo scalar curvature on their boundaries. CAG, 2009 |
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On Characterizations of Isometries on Function Spaces (joint with Yingbin Ruan). Sciences in China, 51(2008), 620--631. |
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On Pseudo-hermitian CR Manifolds. Proceeding of ICCM 2004, Hong-Kong}, to appear |
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On proper harmonic map between two strictly pseudoconvex domains with K\"ahler metrics (with E. Simon), Asian Journal of Mathematics, 11(2007), 251--276. |
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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 |
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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. |
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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 |
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Analysis on Besov spaces II: Embedding and Duality Theorems (with W. Luo), J. of Math. Analysis and Applications, 333 (2007), no. 2, 1189–1202 |
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On characterization of Besov space and application. Part I (with W. Luo). J. of Math. Analysis and Applications, 310(2005), 477-491 |
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Characterization for Balls by Potential Function of Kahler-Einstein Metrics for domains in C^n. Comm. in Analysis and Geometry,} 13(2005), 461--478. |
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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 |
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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 |
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On the Dirichlet problems for the elementary symmetric function equations of the eigenvalues of complex hessian. Asian Journal of Mathematics, 8(2004), 87–106 |
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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 |
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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 |
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Boundary behavior of harmonic functions of Bergman metric on polydisc (with E. Simon) Amer. J. of Math., 124(2002), 1045–1057 |
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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 |
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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 |
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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. |
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On the Existence of Smooth Plurisubharmonic Solutions for Certain Degenerate Monge-Amp`ere Equations (with S. Krantz), Complex variables, 41(2000), 207–219 |
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Applications of the singular integral operators in real and complex analysis, Advance in Math. , China, 29 (2000), 481–501 |
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On the holomorphicity of proper harmonic maps between balls in Cn with Bergman metrics (with L. Ni), Math. Ann., 316 (2000), 333-354 |
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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 |
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On oblique boundary value problems of Monge-Amp`ere equations. Paci?c J. of Math., 190(1999), 155–172 |
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Hankel operators in Dixmier class (with B.Russo), C.R. Acad. Sci. Paris, t. 324, Series 1 (1997), 21–26. |
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On some analysis of function spaces associated with Hankel operators (with S. Krantz and R. Rochberg). Ill. J. of Math., 41(1997), 398–411 |
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On the holomorphic extension of maps from the boundaries of K¨ahler manifolds (with J. Chen). Tohiku Math. J., 49(1997), 585–597. |
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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. |
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On Pseudo-hermitian CR Manifolds. Proceeding of ICCM 2004, Hong-Kong, to appear. |
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On proper harmonic map between two strictly pseudoconvex domains with K\"ahler metrics (with E. Simon), Asian Journal of Mathematics, 11(2007), 251--276. |
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On proper harmonic map between two strictly pseudoconvex domains with Kahler metrics (with E. Simon), Asian Journal of Mathematics, 11(2007), 251–276 |
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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 |
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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 |
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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 |
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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 |
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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 |
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On oblique boundary value problems of Monge-Amp`ere equations. Pacific J. of Math., 190(1999), 155–172 |
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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. |
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On the real analytic hypoellipticity for dbar and dbar_b (with M. Christ). Math. Z., 32(1997), 373-399. |
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Area integral characterizations of functions in Hardy space on domains in C^n (with S. Krantz), Complex variables, 32(1997), 373–399 |
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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. |
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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. |
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The explicit solution for the Lipschitz Corona problem in the polydisc (with S. G. Krantz). Pacific J. of Math., vol iii (1996), 287–302 |
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Characterization of the boundedness for a family of commutators on L^p. Col loquium Math., Vol LXX(1996), 59–71. |
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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. |
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A criteria for composition operators belonging to Schatten trace ideal on Bergman spaces. Amer. J. of Math., 117 (1995), pp 1299-1323. |
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(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. |
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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. |
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A criteria for composition operators belonging to Schatten trace ideal on Bergman spaces, Amer. J. of Math., 117(1995), 1299–1323. |
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On the Neumann problems of complex Monge-Amp`ere equations, Indiana University J. of Mathematics, 44(1995), 1099–1122. |
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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. |
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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. |
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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. |
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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. |
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On the boundedness and compactness of operators of Hankel type (with F. Beatrous) . J. of Functional Analysis, 111 (1993), pp 350-379. |
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Corona problem of several complex variables, Contemporary Mathematics, 137 (1992), 307–328. |
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Toeplitz and Hankel operators on H p (S ) with 0 < p 1, Integral Equations and Operator Theory, 5(1992), 807–824. |
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A Plessner decomposition along transverse curves (with F. Beatrous), Can. J. Math. 5(1988), 1243–1255. |
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Hayman directions of meromorphic functions in the complex plane, Acta Math. Sinica Series (2), 4(1988), 97–110. |
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On normal families of meromorphic functions (with H. Xie), Acta Math. Sinica 4(1986), 468–476. |
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| A note on Bloch law, J. Math. Res. Expo. 2(1986), 10–11. | ||
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On the distributions of the singular directions of gap entire functions, J. Fujian Normal Univ. 2(1986), 1–7. |
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Moduli distribution and normal families (with H. Xie), Pure and Appl. Math. (China) 1(1986), 57–67. |
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On normal families of meromorphic functions (with H. Xie), Advance in Math., China 1(1985) 71–73. |
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| On a normal criteria of a class of functions, J. Fujian Normal Univ. 1(1984), 153–158. | ||
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On normal families and singular directions of meromorphic functions with multiplicity values, J. Fujian Normal Univ. 1(1984), 21–38. |
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Professional Society |
AMS |
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| Link to this profile | http://www.faculty.uci.edu/profile.cfm?faculty_id=4833 | |
| Last updated | 01/27/2009 | |