THE -PROBLEM FOR HOLOMORPHIC (0,2)-FORMS ON PSEUDOCONVEX DOMAINS IN SEPARABLE HILBERT SPACES AND D.F.N. SPACES
THE -PROBLEM FOR HOLOMORPHIC (0,2)-FORMS ON PSEUDOCONVEX DOMAINS IN SEPARABLE HILBERT SPACES AND D.F.N. SPACES
摘要
This paper shows that the 8-problem for holomorphic (0, 2)-forms on Hubert spaces is solv-able on pseudoconvex open subsets. By using this result, the authors investigate the existence of the solution of the -equation for holomorphic (0, 2)-forms on pseudoconvex domains in D.F.N. spaces.
基金
The first author was supported by KOSEF postdoctoral fellowship 1998 and the second author was supported by the Brain Korea 21 P
参考文献14
-
1Colombeau, J. F. & Perrot, B.,L'équation dans les ouverts pseudo-convexes des espaces D. F. N. [J],Bull. Soc.Math. France, 110 (1982), 15-26.
-
2Dineen, S., Cousin's first problem on certain locally convex topological vectorspaces [J], 48:1(1976),An. Acad. Brasil Ciénc, 11-12.
-
3Hormander, L., Introduction to complex analysis in several variables [M],North-Holland, Amsterdam,1990.
-
4Kajiwara, J. & Li, L., Reproducing kernels for infinite dimensional domains[A], Proceedings of the Fifth International Colloquium on Differential Equations [C], VSP(Utrecht) (1994), 153-162.
-
5Lee, J. & Shon, K. H., The -problem related to finite and infinite dimensionalcomplex spaces [J],Korean Journal of Math. Sci., 4(1997), 177-182.
-
6Lee, J. & Shon, K. H., The -equation in Cn for holomorphic (0, 2)-forms definedon infinite dimensional spaces [J], 62:2(1998), Par East J. of Math. Sci., 241-250.
-
7Mazét, P., Un théorème d'hypoellipticité pour l'opérateursur les espaces de Banach [J], 292:1(1981),C. R. Acad. Sci. Paris Ser. L Math., 31-33.
-
8Nishihara, M., On the indicator of growth of entire functions of exponential typein infinite dimensional spaces and the Levi problem in infinite dimensional projectivespaces [J], Portugaliae Math. 52(1995),61-94.
-
9Nishihara, M., Kajiwara, J., Li, L. & Yoshida, M., On the Levi problem forholomorphic mappings of Riemann domains over infinite dimensional spaces into a complexLie group [J], 26:2(1994), Res. Bull.Fukuoka Inst. Tech., 151-161.
-
10Pietsch, A., Nuclear locally convex spaces [M], Erg. der Math. 66, SpringerVerlag, 1972.
-
1史济怀.Bergman type operators on a class of weakly pseudoconvex domains[J].Science China Mathematics,1998,41(1):22-32.
-
2马忠泰.THE EXPLICIT SOLUTIONS OF C_(p,q)^(k+α)-FORM FOR THE -EQUATIONS ON PSEUDOCONVEX OPEN SETS[J].Acta Mathematicae Applicatae Sinica,1997,13(2):130-135. 被引量：3
-
3钟同德._b-EQUATION ON COMPLEX MANIFOLDS[J].Acta Mathematica Scientia,1997,17(3):262-268.
-
4叶轩,张锦豪.THE EXISTENCE OF μ-HOLOMORPHIC SEPARATING FUNCTION ON BOUNDED SMOOTH DOMAINS[J].Chinese Annals of Mathematics,Series B,1992,13(4):406-410.
-
5盛保怀,刘三阳.THE OPTIMALITY CONDITIONS OF NONCONVEXSET-VALUED VECTOR OPTIMIZATION[J].Acta Mathematica Scientia,2002,22(1):47-55. 被引量：2
-
6Jinxiu XIA,Tongde ZHONG,Chunhui QIU.Laplacian on Complex Finsler Manifolds[J].Chinese Annals of Mathematics,Series B,2011,32(4):507-520. 被引量：1
-
7GONG Ding-dong Dept.of Math.,Zhejiang Univ.,Hangzhou 310027,China,Dept.of Math.Sci.,Zhejiang Sci-Tech Univ.,Hangzhou 310018,China..Singular integral on bounded strictly pseudoconvex domain[J].Applied Mathematics(A Journal of Chinese Universities),2008,23(3):273-278. 被引量：1
-
8Heungju AHN,Hong Rae CHO,Jong-Do PARK.Non-isotropic weighted L^p estimates for the -equation on piecewise smooth strictly pseudoconvex domains[J].Science China Mathematics,2008,51(12):2161-2171.
-
9Yihong HAO.Canonical Metrics on Generalized Cartan-Hartogs Domains[J].Chinese Annals of Mathematics,Series B,2016,37(3):357-366.
-
10J.KAJIWARA,LIXIAODONG,K.H.SHON.COHOMOLOGY VANISHING IN HILBERT SPACES[J].Chinese Annals of Mathematics,Series B,2004,25(1):87-96.
