The Pointwise Multipliers From Space F(p, g, s) to Bloch Type Space in Cn

1 IntroductionLet B be the unit ball in Cn. By H(B) we denote the class of all holomorphic functions on B and H∞ denotes the class of all bounded holomorphic functions on B .For α ∈ B , let g(z,α) = log |ψα(z)|-1 be Green's function for B with logarithmic singularity at a, where ψα is the Mobius transformation of B satisfying ψα(0) =α,ψα(α) =0, ψα = ψα-1.Difinition 1 Let 0 < p. s < ∞, -n - 1 < q < ∞. We say f ∈ F(p, q, s) provided that     

Fekete and Szeg problem in one and higher dimensions

In this paper, we establish the Fekete and Szeg inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in C~n.     

WEIGHTED HOLOMORPHIC BESOV SPACES AND THEIR BOUNDARY VALUES

We study weighted holomorphic Besov spaces and their boundary values. Under certain restrictions on the weighted function and parameters, we establish the equivalent norms for holomorphic functions in terms of their boundary functions. Some results about embedding and interpolation are also included.     

The Coefficient Inequalities for a Class of Holomorphic Mappings in Several Complex Variables

The authors establish the coefficient inequalities for a class of holomorphic mappings on the unit ball in a complex Banach space or on the unit polydisk in ■~n,which are natural extensions to higher dimensions of some Fekete and Szeg? inequalities for subclasses of the normalized univalent functions in the unit disk.     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

A COUNTEREXAMPLE ON MONOTONE MuNTZ APPROXIMATION Ⅱ

We adopt the following symbols and notations. Let C_([0,1])~N be the class of all real continuous functions in [0,1] which have N continuousderivatives, L_[0,1]~p be the space of real pth power integrable functions on [0,1], and Δ~k, asusual, be the class of kth monotone functions.     

THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN C2

k holomorphic functions are a type of generation of holomorphic functions. In this paper, a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in C². The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel. Furthermore, the integral representation for the solution is obtained.     

A Note on Schwarz-Pick Estimate

A Schwarz-Pick estimate of higher order derivative for holomorphic functions with positive real part on Bn is presented. This improves the earlier work on Schwarz-Pick estimate of higher order derivatives for holomorphic functions with positive real part on the unit disk in C.     

Analytic Properties for Holomorphic Matrix-valued Maps in C~(2×2)

In this paper, we investigate some analytic properties for a class of holomorphic matrixvalued functions. In particular, we give a Picard type theorem which depicts the characterization of Picard omitting value in these functions. We also study the relation between asymptotic values and Picard omitting values, and the relation between periodic orbits of the canonical extension on C~(2×2) and Julia set of one dimensional complex dynamic system.     

SCHWARZ-PICK ESTIMATES FOR BOUNDED HOLOMORPHIC FUNCTIONS ON CLASSICAL DOMAINS

In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of higher order partial derivatives for bounded holomorphic functions on the disk and unit ball.     

Space curve evolution,geometric phase,and solitons

Certain moving space curves are endowed with a geometric phase. This phase arises due to the path dependence of the rotation of an orthonormal triad (frame) defined at every point on the curve. In the present work we use the connection between moving curves and soliton dynamics to find the geometric phase associated with a class of soliton-supporting equations.The Institute of Mathematical Sciences, C.I.T. Campus, Madras 600 113, India. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 99, No. 2, pp. 172–176, May, 1994.     

Tiling Space by Platonic Solids, I

There exist precisely 914, 58, and 46 equivariant types of tile-transitive tilings of three-dimensional euclidean space by topological cubes, octahedra, and tetrahedra, that fall into 11, 3, and 9 topological families, respectively. Representatives are described for all topological families. A general method for obtaining results of this kind is introduced. Received February 13, 1997, and in revised form September 17, 1997.     

Chiral Polyhedra in Ordinary Space, I

Chiral polyhedra in ordinary euclidean space E³ are nearly regular polyhedra; their geometric symmetry groups have two orbits on the flags, such that adjacent flags are in distinct orbits. This paper completely enumerates the discrete infinite chiral polyhedra in E³ with finite skew faces and finite skew vertex-figures. There are several families of such polyhedra of types {4,6}, {6,4} and {6,6}. Their geometry and combinatorics are discussed in detail. It is also proved that a chiral polyhedron in E³ cannot be finite. Part II of the paper will complete the classification of all chiral polyhedra in E³. All chiral polyhedra not described in Part I have infinite, helical faces and again occur in families. So, in effect, Part I enumerates all chiral polyhedra in E³ with finite faces.     

Chiral Polyhedra in Ordinary Space, II

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary euclidean space E³ with finite skew faces and finite skew vertex-figures; they occur in infinite families and are of types {4,6}, {6,4} and {6,6}. Part II completes the enumeration of all discrete chiral polyhedra in E³. There exist several families of chiral polyhedra of types {∞,3} and {∞,4} with infinite, helical faces. In particular, there are no discrete chiral polyhedra with finite faces in addition to those described in Part I.     

广义加权Bloch空间与QK(p,q)空间之间的复合算子

设φ是复平面上的单位圆盘D上的全纯自映射,0＜p＜∞,q＞-2,α＞0.本文给出广义加权Bloch空间与QK(p,q)空间之间的复合算子的有界性和紧性.     

Torsion-Free Space Groups, 2-Cohomology, and Scott Modules

For a subgroupCof orderpof a finite groupG, we find the summandMof thep-adic permutation module ind_C^GZ_psuch thatH²(G, M)≠0, and determine whenMis the Scott module. This is applied to the study of torsion-free space groups.     

On Quasiperiodic Space Tilings, Inflation, and Dehn Invariants

We introduce Dehn invariants as a useful tool in the study of the inflation of quasiperiodic space tilings. Tilings by ``golden tetrahedra' are considered. We discuss how Dehn invariants can be applied to the study of the inflation properties of the six golden tetrahedra. We also use the geometry of the faces of the golden tetrahedra to analyze their inflation properties. We give inflation rules for decorated Mosseri—Sadoc tiles in the projection class of tilings <I>T<SUP>(MS)</SUP></I> (the tiles of <I>T<SUP>(MS)</SUP></I> are particular packages of the golden tetrahedra). The Dehn invariants of the Mosseri—Sadoc tiles provide two eigenvectors of the inflation matrix with eigenvalues equal to \t = (1+\sqrt 5 )/2 and -1/\t , and allow us to reconstruct the inflation matrix uniquely. Received October 11, 1999, and in revised form July 5, 2000. Online publication May 4, 2001.     

Quantum Real Projective Space, Disc and Spheres

We define the C ^*-algebra of quantum real projective space R P _q ², classify its irreducible representations, and compute its K-theory. We also show that the q-disc of Klimek and Lesniewski can be obtained as a non-Galois Z ₂-quotient of the equator Podle quantum sphere. On the way, we provide the Cartesian coordinates for all Podle quantum spheres and determine an explicit form of isomorphisms between the C ^*-algebras of the equilateral spheres and the C ^*-algebra of the equator one.