Equivalences between bloch type spaces and BOM spaces on the hyperbolic domains inC

For an analytic function f on the hyperbolic domain Ω inC, the following conclusions are obtained: (i) f∈B(Ω)=BMO A(Ω,m) if and only ifRef∈B_h(Ω)=BMOH(Ω,m). (ii) QB_h(Ω)=B_h(Ω)(BMOH _n(Ω,m)=BMOH(Ω,m)) if and only ifC(Ω)=inf{λ_Ω(z)·δ_Ω(z):z∈Ω}>0. Also, some applications to automorphic functions are considered. This research was supported by the Doctoral Program Foundation of Institute of Higher Education.     

Indices of Toeplitz tuples on pseudoregular domains

This paper proves an index theorem of Toeplitz tuples on pseudoregular domains in Cn. Geometrically, the index of Toeplitz tuple TΦn is (-1)n time wrapping number of Φn around the origin. As one of the applications of the index theorem, we completely characterize the automorphism groups of Toeplitz algebras on Poincaré domain. As another application, it is shown that C*(Ω)C*(Bn) for every Poincare domain Ω in Cn(n≠2). It is also noticed that C*(Ω)C*(B2) if and only if the Poincaré conjecture is true for Ω.     

Weighted composition operators on growth spaces

Denote by Hol(B _n ) the space of all holomorphic functions in the unit ball B _n of ℂ ⁿ , n ≥ 1. Given g ∈ Hol(B _m ) and a holomorphic mapping φ: B _m → B _n , put C _φ ^g f = g · (f ∘ φ) for f ∈ Hol(B _n ). We characterize those g and φ for which C _φ ^g is a bounded (or compact) operator from the growth space A ^−log(B _n ) or A ^−β (B _n ), β > 0, to the weighted Bergman space A _α ^p (B _m ), 0 < p < ∞, α > −1. We obtain some generalizations of these results and study related integral operators.     

On Almost Isometric Embedding from C（Ω） into C0（Ω0）

In this paper we give the sufficient and necessary condition for the existence of any almost isometric operator from C（Ω） into C0（Ω0）. As a corollary, we show that there is no e-isometry from 1 any abstract M space with a strong unit into C0（Г） if 0 〈 e 〈 1/9.     

Boundedness of commutators for Marcinkiewicz integrals on weighted Herz-type Hardy spaces

In this paper,the authors study the boundedness of the operator μ b Ω,the commutator generated by a function b ∈Lip β (R n)(0 < β < 1) and the Marcinkiewicz integral μΩ on weighted Herz-type Hardy spaces.     

The affine complete hypersurfaces of constant Gauss-Kronecker curvature

Given a bounded convex domain Ω with C∞ boundary and a function ψ∈C∞（δΩ）, Li-Simon-Chen can construct an Euclidean complete and W-complete convex hypersurface M with constant affine Gauss-Kronecker curvature, and they guess the M is also affine complete. In this paper, we give a confirmation answer.     

Spectra of weighted composition operators on algebras of analytic functions on banach spaces

Let E be a complex Banach space, with the unit ball B _E . We study the spectrum of a bounded weighted composition operator u C _φ on H ^∞(B _E ) determined by an analytic symbol φ with a fixed point in B _E such that φ(B _E ) is a relatively compact subset of E, where u is an analytic function on B _E .     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalized absolute Cesaro summability of a Fourier series

In an attempt to study the scope of a theorem due to Pati, the authors have established that φ(t) logK|t∈B _u V in (0,π)⟹ΣA _n (x) is |C, 0,β| forβ>1, at the pointt = x.     

On the Bloch Constant for Κ-Quasiconformal Mappings in Several Complex Variables

We study the Bloch constant for Κ-quasiconformal holomorphic mappings of the unit ball B of C ⁿ . The final result we prove in this paper is: If f is a Κ-quasiconformal holomorphic mappig of B into C ⁿ such that det(f′(0)) = 1, then f(B) contains a schlicht ball of radius at least where C _n > 1 is a constant depending on n only, and as n→∞. Received June 24, 1998, Accepted January 14, 1999