摘要:

Nonlinear Riemann-Hilbert problems for first and second order elliptic system have been studied by many authors. They usually apply Schauder's fixed point theorem to prove the existence of a Hölder continuous solution in the Sobolev space. In [1, 2] L.V. Wolfersdorf discusses a class of nonlinear Riemann-Hilbert problems for holomorphic functions with monotone nonlinearity and proves the existence of a solution in W12. In [3] R.P Gilbert and Li Mingzhong further discuss the existence of solution from W12for generalized analytic functions and first-order nonlinear elliptic system where the proof of existence of a solution in W12has been established.

ISSN:0278-1077    

DOI:10.1080/17476939708814983

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We show that holomorphic functions inare characterized by a special mean-value condition, and also indicate a new mean-value characteristic for pluriharmonic functions, that is real parts of holomorphic functions.

ISSN:0278-1077    

DOI:10.1080/17476939708814984

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

It is proved that pointwise inequalities on a finite set of concentric circles of the unit disk are enough to secure norm inequalities in the Bergman space L2ain the case of the lower function being a polynomial. The radii of the circles are connected to the zeroes of the Jacobi polynomials. The method of proof extends the result to statements on the spaces L2maand as well as some weighted spaces. Furthermore only inequalities between integral means are necessary. The result interpreted as restriction operators to unions of circles is then generalized to many Lpa

ISSN:0278-1077    

DOI:10.1080/17476939708814985

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

LetAdenote the class of functionsthat are analytic in the unit disc:IffεAandwhere M0is the strictly positive solution of the equationthenorZεUand this result is sharp.

ISSN:0278-1077    

DOI:10.1080/17476939708814986

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

For the classAof normalized regular functionsf(z)in the unit disc withf(0)=0fprime(0)=1 setsto be a neighborhood off. We determine here (in certain cases sharp) radii ofUδ (f) such that some integral operators carry the neighborhood into the classS, fbelonging to universal linear invariant families or to well-known subclasses of univalent functions.

ISSN:0278-1077    

DOI:10.1080/17476939708814987

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper, the unicity theorems for meromorphic functions that share a pair of small functions has been studied. This also generalizes the Nevanlinna's four values theorem and some results about meromorphic functions sharing three values in and [8] and [9]

ISSN:0278-1077    

DOI:10.1080/17476939708814988

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor