摘要:

This article is primarily interested in the question of whether it is possible to characterize the spaceDˆ, the space of Fourier transforms ofCinfinfunctions with compact support, by the distribution of the zeros of the functions. The first two theorems deal with the case of sin(πz) divided by some entire function, and the last theorem generalizes this somewhat.

ISSN:0278-1077    

DOI:10.1080/17476939408814750

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

It is shown that every entire function of exponential type not belonging to Akhlezer's class has a divisor of zero exponential type with the same property. Tlus basic fact allows one to establish a connection between uniqueness theorems for entire functions of exponential type and Akhiezer's class.

ISSN:0278-1077    

DOI:10.1080/17476939408814751

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

We characterize VMO on the unit sphere ofby means of the Garsia norm and by the actions of the unitary group, with which we then characterize VMOA on the unit ball by vanishing Carleson measures. Analogues for BMOA were given by Choa and Choe [1] and by Jevtić [5].

ISSN:0278-1077    

DOI:10.1080/17476939408814752

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In a recent paper spaces of holomorphic functions on tubes inwhich generalize the HardyHpspaces on tubes were defined and studied using the theory of ultra-distributions. UsingLptheory of Fourier transforms Cauchy and Poisson integral representations of these functions were obtained and existence ofS′(Mk;Mk)-boundary values of generalizedHp-functions was established for 1 <p≤ 2. In this paper some of these results are extended to the case 2 <p< ∞. A Poisson integral representation is given and a sufficient condition for a function in the generalized space to be inHp-space is obtained in terms of itsS′(Mk;Mk)-boundary value.

ISSN:0278-1077    

DOI:10.1080/17476939408814753

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Let Γ be a torsion free Fuchsian group with parabolic elements andTΓ be of infinite dimension. We prove that the Carath´odory metric and the Teichmüller metric onTΓ do not coincide. This answers partially a problem posed by Abikoff in 1974.

ISSN:0278-1077    

DOI:10.1080/17476939408814754

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

The purpose of this paper is to discuss the stability of Bergman metric and Caratheodory metric in the deformation.

ISSN:0278-1077    

DOI:10.1080/17476939408814755

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Letfbe a quasiconformal self-mapping of the complex plane. We introduce a notion of asymptotical homogeneity of the mappingfat the prescribed point and in these terms give equivalent conditions forquasi conformal curves to be asymptotically conformal. The proofs are based on a fundamental geometrical criterion of asymptotically conformal curves obtained by Ch. Pommerenke and J. Becker.

ISSN:0278-1077    

DOI:10.1080/17476939408814756

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

It is a well known fact that the Newtonian potential of a uniform mass distribution in an ellipsoid is equal to a quadratic polynomial inside the ellipsoid. Conversely, ifKis a bounded solid inRmand its Newtonian potential is equal to a quadratic polynomial inside it, thenKis an ellipsoid. P. Dive proved this result form=3 in 1931, and in 1986 E. DiBenedetto and A. Friedman showed it to be true for allm≥ 2. We use certain topological methods to obtain a simpler proof of this result.

ISSN:0278-1077    

DOI:10.1080/17476939408814757

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this article, we consider the spaceBp(D) (resp. ß) of functionswherehandkare holomorphic in a domainDinof classC3andfis inLp(D) (resp. the derivatives offof order 2 are majorized by the reciprocal of the square of distance to the boundary). We ask when the dual of B1can be identified with the space ß. In the case of holomorphic functions, B. Coupet has proved that the dual of the space of holomorphic functions, integrable over a strictly pseudoconvex domainDinof classC3can be identified with the Bloch space ß of holomorphic functions inDsuch thatfor everyzinD. First, following Bell's methods [1] we define the duality betweenB1and ß we prove that there exists a differential operatorLof order 2 continuous from ß toL∞ such that, ifPis the Bergman projection ofL2intoB2PLis equal to identity. This allows us to extend toB1×Bthe bilinear form on. Secondly, we prove that ß and the dual ofB1are isomorphic if and only if (1):B2is dense inB1and (2):PmapsL∞ intoB. In this case there exists a continuous projection ofL1intoB1. Following Carmona we prove that (1) is true for every open setDofsuch thathas a finite number of connected components, and that (2) can be expressed by estimations on the Bergman kernel forB2:We conclude that in the case of the unit disc, ß and the dual ofB1are isomorphic.

ISSN:0278-1077    

DOI:10.1080/17476939408814758

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939408814749

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor