摘要:

In this paper we prove an extension of an estimate first proved by Ahern and Bruna of the modulus of absolute continuity holomorphic functions have on real analytic curves in the unit ball to a certain class of smooth curves satisfying a finite type condition. We then show that this yields insights into the sharpness of recent formulations of Privalov's theorem in the unit ball and in particular to the existence of counterexamples on flatC2−εcurves.

ISSN:0278-1077    

DOI:10.1080/17476939608814967

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

It has been proved in the paper [4] that provided a space of pseudoholomorphic functions is given, one can construct operatorsLsuch that the initial value problem of Cauchy-Kowalewski typeturns out to be solvable by the abstract Cauchy-Kowalewski theorem in any case. Moreover the solution belongs to the associated space defined by the ordinary differential equation of the formwheredenotes theE-derivative of theE-pseudoholomorphic function ω − ω(t, z) in the sense of Bers [1], and α(z) and β(z) are to be chosen suitably.

ISSN:0278-1077    

DOI:10.1080/17476939608814968

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We consider conformal maps of the unit disk onto a bounded domain in the complex plane. The average growth of the derivative of such functions is described by the integral means spectrum. There are only partial results about finding sharp estimates. We use Fatou sets of quadratic polynomials as image domain to get an indication for better estimates. The results of a computer search lead to a conjecture abouth the shape of the universal integral means spectrum. This includes some previous and other contecture the Brennan conjecture and the Carleson Jones contecture concerning the coefficient problem.

ISSN:0278-1077    

DOI:10.1080/17476939608814969

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

LetD1,D2,…Dmbe anympartial derivative operators inwith the formwherej= (j1,j2,…jn) is a multi-index. Suppose thatfis an entire function inthat is a solution of the partial functional-differential equationF(D1y,D2y,…Dmy)= 0, whereFis an entire function inor more generally, a formal power series inD1y,D2y,…Dmywith coefficients being small functions offWe give in this paper a reduction theorem which shown whenfa solution of a much simpler equationP(D1y,D2y,…Dmy= 0, wherePis a non-zero polynomial inD1y,D2y,…Dmy.

ISSN:0278-1077    

DOI:10.1080/17476939608814970

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We give a geometric description of contmuaKin the complex plane consisting of two closed Jordan domains touching at the origin with the following property: The uniform polynomial approximation onKto a complex extension of the modulus functions has the same other as in the case of the unit interval [-1 1]of the real axis.

ISSN:0278-1077    

DOI:10.1080/17476939608814971

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

The object of this paper is to present generalizations of some recent results ot S.S. Miller and P.T. Mocanu on the univalence and starlikeness of Kummer' confluent hypergeometric function. Some applications involving generalized hypergeometric functions associated with the Hardy space of analytic functions are also considered.

ISSN:0278-1077    

DOI:10.1080/17476939608814972

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We prove that, if ρ is a boundary point of a smoothly bounded pseudoconvex Reinhardt domain in, then the variety type at ρ is identical to the regular type.

ISSN:0278-1077    

DOI:10.1080/17476939608814973

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939608814966

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor