一类有界对称域上的Hartogs型域的自同构群

本文研究了稍微广泛的一类Hartogs型域的自同构群.利用华域的自同构群,获得了一类有界对称域上的Hartogs型域的自同构群的具体形式,推广了有界对称域上的Hartogs型域的自同构群这一结果.     

Symmetry of integral equation systems on bounded domains

In this paper, we investigate the symmetry of domains and solutions of integral equation systems on bounded domains. Under some natural integrability conditions, we prove that the domains are balls, all positive solutions of systems are radially symmetric and monotone decreasing with respect to the radius.     

Symmetry of integral equation systems with Bessel kernel on bounded domains

In this paper, we investigate the symmetry of integral equation systems with Bessel kernel on bounded domains. Under some natural integrability conditions, we prove that the domains are balls and all positive solutions are radially symmetric and monotonic decreasing.     

C~n中具有逐块光滑边界的有界域上带权因子积分表示的拓广式

本文讨论了Cn空间中具有逐块光滑边界的有界域上和强拟凸域上具有拓广的B-M核的(0,q)形式的带权因子的积分表示式,得到了带权因子拓广的Koppelman- Leray-Norguet公式．由此得到了有界域上-方程带权因子的连续解,由于权因子的引入,使得积分公式在应用上(如在函数插值问题的应用)具有更大的灵活性．     

Sobolev spaces on bounded symmetric domains

We obtain a formula for the Sobolev inner product in standard weighted Bergman spaces of holomorphic functions on a bounded symmetric domain in terms of the Peter–Weyl components in the Hua–Schmidt decomposition, and use it to clarify the relationship between the analytic continuation of these standard weighted Bergman spaces and the Sobolev spaces on bounded symmetric domains.     

关于有界对称域上的混合范数空间

本文研究了Ｃｎ中有界对称域Ω上的混合范数空间Ｈ（ｐ，ｑ，　）其中０＜ ｐ＜　，０＜ｑ＜　，　是正规函数，给出了Ω上全纯函数ｆ的分数导数ｆ［β］和 分数积分ｆ［β］属于（ｐ，ｑ，）的等价条件。应用这些结果，就两种情形０＜ｐ≤２， ０＜ｑ＜　和２≤ｐ＜，０＜ｑ＜ ，用全纯函数ｆ的展式中的系数，分别给出了 ｆ　Ｈ（ｐ，ｑ，）的必要条件和充分条件，并证明了多调和函数ｕ组成的混合范数空 间ｈ（ｐ，ｑ，）（０＜ｐ，ｑ＜　）是自共轭的．     

Existence and multiplicity of solutions for critical elliptic equations with multi-polar potentials in symmetric domains

In this paper, we consider the elliptic equations with critical Sobolev exponents and multi-polar potentials in bounded symmetric domains and prove the existence and multiplicity of symmetric positive solutions by using the Ekeland variational principle and the Lusternik–Schnirelmann category theory.     

The K(a)hler-Einstein metric for some Hartogs domains over symmetric domains

We study the complete K(a)hler-Einstein metric of a Hartogs domain (Ω) built on an irreducible bounded symmetric domain Ω, using a power Nμ of the generic norm of Ω. The a boundary condition. The domain (Ω) is in general not homogeneous, but it has a subgroup of automorphisms, the orbits of which are parameterized by X ∈ [0, 1[. This allows us to reduce the can be explicitly solved for a special valueμ0 ofμ. We work out the details for the two exceptional symmetric domains. The special value μ0 seems also to be significant for the properties of other invariant metrics like the Bergman metric; a conjecture is stated, which is proved for the exceptional domains.     

A new Leray formula for smooth functions on bounded domains in Cn

By means of a new technique of integral representations in Cn given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in Cn, which is different from the well-known Leray formula, This new formula eliminates the term that contains the parameter λ from the classical Leray formula, and especially on some domains the uniform estimates for the -equation are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in Cn, which are different from the classical ones, when we properly select the vector function W.     

带Bergman度量的有界典型域上Laplace-Beltrami算子谱的下界

本文估计了带K?hler度量的有界典型域上Laplace-Beltrami算子谱的下界,给出了带K?hler度量的第二类有界典型域上Laplace-Beltrami算子谱的下界的范围.特别地,对于秩为1的区域,本文给出的结论与已有结论相一致.     

Weighted composition operators on weighted Bergman spaces of bounded symmetric domains

In this paper, we study the weighted compositon operators on weighted Bergman spaces of bounded symmetric domains. The necessary and sufficient conditions for a weighted composition operator W _φψ to be bounded and compact are studied by using the Carleson measure techniques. In the last section, we study the Schatten p-class weighted composition operators.     

Bloch spaces on bounded symmetric domains in complex Banach spaces

We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

Bloch spaces on bounded symmetric domains in complex Banach spaces Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.     

SMALL HANKEL OPERATORS ON WEIGHTEDBERGMAN SPACES OF BOUNDED SYMMETRIC DOMAINS

1IntroductionLetnbeaboundedsynunetricdomaininC"withBerg1llankernelK(z,w),fldenotestheEuclideanclosureofninCnandoflistheTopologicalboundaryWeassumethatnisinitsstandardrepresentationandthevolumemeasuredVofflisuormalized.Itfollowsfrom[1],[2]thatthekernelfullctionsK(-,.)havethespecialproperties:(l):K(O,w)=K(z,o)=l,z,wEfl;(2):K(z,w)/o1zEfl,wEfl;(3):.13hK(z,z)=oo;(4):K(z,w)-'isasmoothfunctiononC',xC".ofcourse,K(z,w)=K(w,z).Thecomplexcol1jugateoffisdenotedbyf.By5.7of[3]andpolarcoordinates,th…     

Spectral Gap for Stable Process on Convex Planar Double Symmetric Domains

We study the semigroup of the symmetric α-stable process in bounded domains in R ². We obtain a variational formula for the spectral gap, i.e. the difference between two first eigenvalues of the generator of this semigroup. This variational formula allows us to obtain lower bound estimates of the spectral gap for convex planar domains which are symmetric with respect to both coordinate axes. For rectangles, using “midconcavity” of the first eigenfunction (Bañuelos et al., Potential Anal. 24(3): 205–221, 2006), we obtain sharp upper and lower bound estimates of the spectral gap.     

有界对称域上的BO空间的乘子

本文给出了有界对称域上的有界振动函数（ＢＯ）空间的点态乘子的刻划。     

THE BLOCH CONSTANT OF LOCALLY BIHOLOMORPHIC MAPPINGS ON BOUNDED SYMMETRIC DOMAINS

51.IntroductionIn[11,westudiedtheboundsofBlochconstantofholomorphicmappingsonirreducibleboundedsymmetricdomains.ThispaperisasuccessivepaPerof[1].WestudytheboundsoftheBlochconstantoflocallybiholomorphicmappingsonirreducibleboundedsymmetricdomains.AllthenotationsofthispaPerarethesameasthoseweusedin[1].LetDbeadomain,whichcontainstheorigin.AholomorphicmappingonDisdefinedasaBlochmappingifthefamilyofmappingsFj={g:g(z)=f(rk(z))-j(gh(o)),forallrkEAut(D)},isanormalfamily.TheBlochnormofaBlochmapp…     

~n中有界域上全纯函数的第Ⅰ型 C-F公式

本文得到Ｃｎ中有界域上全纯函数的一种其积分密度函数含有全纯函数导数的 Ｃａｕｃｈｙ－Ｆａｎｔａｐｐｉ　　公式，称之为第Ⅰ型 Ｃ－Ｆ 公式，利用这个公式，通过适当选择其中的向量函数，可以得到许多区域上全纯函数相应的第Ⅰ型积分表示式．     

A topological Maslov index for 3-graded lie groups

Motivated by the generalization of the Maslov index to tube domains and by numerous applications of related index function in infinite-dimensional situations, we describe in this paper a topologically oriented approach to an index function generalizing the Maslov index for bounded symmetric domains of tube type to a variety of infinite-dimensional situations containing in particular the class of all bounded symmetric domains of tube type in Banach spaces. The framework is that of 3-graded Banach-Lie groups and corresponding Jordan triple systems.