摘要:

Let ρ(z) denote the Poincaré metric onC– {0,1}. It is known thatwhere λ(τ) is the elliptic modular function We define the functionWe obtain the following mequalitics:, where 0≦x≦ 1 by using the above inequalities and Poincaré metric. we get a new version of Schottky' theorem.

ISSN:0278-1077    

DOI:10.1080/17476939008814387

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

We will treat mainly the class of equation of the formwherePandQare polynomials ofw′i>wrespectively.pandqdenote degree ofP(z,w′)andQ(z,w)with respect tow′andwrespectively. We prove the following theorem.

ISSN:0278-1077    

DOI:10.1080/17476939008814388

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

LetDbe an open subset of RNN≧ 2, such thatO∈Dand λ(D) < + ∞, where λ denotesN-dimensional Lebesgue measure. If the mean-value equalityholds for every integrable harmonic functionhonD. then accoeding to a theorem of KuranDis a ball of centreO. Here we show that the same conclusion holds if we assume the above mean-value equality only for positive integrable harmonic functions. Further, if the mean-value equality is assumed only for bounded harmonic functions, thenD=B=\E, whenBis an open ball andEis a polar set.

ISSN:0278-1077    

DOI:10.1080/17476939008814389

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

In this paper we develop a plane system of first-order differential equations, describing nullsolutions of the Dirac operator in biaxially symmetric domains. The solutions to the equations are of pseudoanalytic type and may be used to construct on orthogonal basis for the spaces of so-called spherical monogenics. which are related to spherical harmonics with spin. Finally, after certain restrictions on dimensins. We give a complete characterization of these pscudoanalytic functions in terms of holomorphic ones. This paper may thus ge considered as a bridge between Clifford analysis and the theory of pscudoanalytic functions.

ISSN:0278-1077    

DOI:10.1080/17476939008814390

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

An integral mean inequlity for Hadamard products of functions holomorphic on the diskDhas been recendly proved by M Pavlovic. We give a natural generalization to the polydiscDnwhere 0 <p≦ 1p≧q< ∞ andf*gis the Hadamard product off∈Hpandg∈Hq.

ISSN:0278-1077    

DOI:10.1080/17476939008814391

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

Letdbe a positive integer andd≧ 2. ForK⊂Cd+ 1O(K) denotes the spaces of germs of holomorphic functions onKandO(K) denotes the dual spaces ofO(K) The Fantappié indicatoris defined by, wherePd + 1(C) is the complex projective space of (d+ 1) dimensions. A. Martineau determined the image ofO(K) by the transformation Φ:T→ Φ1for the case whereKis convex and compact. We consider the unit sphereSRd+ 1. Martineau's result cannot apply forO′(S) becauseSis not convex. We will determine, in this paper, hte image ofO′(S) by Φ.

ISSN:0278-1077    

DOI:10.1080/17476939008814392

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

The paper is concerned with linear differential equations, essentiallywhereof order 2nfor holomorphic functionsuof 2ncomplex variableswe derive power series expansions for the generating functions for mtegral operators of generalized Vekua's and Bergman's type (called Ricmann function and Bergman kernel respectively). which permit integral representations of the solutionsu. In case of the above mentioned equation these generating functions are shown to be associated by complex iontegrat transformations.

ISSN:0278-1077    

DOI:10.1080/17476939008814393

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939008814394

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

The boundedness criterion for Hankel forms over a plane domain of connectivity two, derived in a previous paper (Complex Variables10 (1988), 123-139). is extended to the case of higher connectivity. The main result is however that the relevant reproducing kernel extends meromorphically to the Schottly double of the domain, and this again implies the desired weak factorization.

ISSN:0278-1077    

DOI:10.1080/17476939008814395

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

Letfbe analytic and bounded in the unit diskB2or quasiconformal in the unit ballBnof, and letz0be a boundary point ofB2orBn. We assume thatfor a suitable majornat μ and for allzon ∂B2whenfis analytic, or for allzon an from 0 toz0whenfis quasiconforml. We then obtain estimates forwhenz1andz2lie in a Stolz angle or cone with vertex atz0.

ISSN:0278-1077    

DOI:10.1080/17476939008814396

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor