摘要:

In an earlier paper in this journal, Andnevskii [l] studied the following question. LetGandGbe two disjoint domains “touching” atz= 0.letf(z)−zinG+andf(z)inG−. What is the errorEnof approximation offby polynomials of degree ≦ninG+UG−? We give a less technical and more constructive approach to this problem and generalize it tof(z) = z∞inG−andf(z)= (−z)∞inG−, and we admit more general types of touching domains.

ISSN:0278-1077    

DOI:10.1080/17476939708815057

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In this paper we give boundedness criteria for generalized Hankel operators Hf,jand H'f,j

ISSN:0278-1077    

DOI:10.1080/17476939708815058

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The holomorphic sectional curvatures under invariant Kahler metrics on certain pseudoconvex domains E(m, n, K) are given in the explicit forms. In the meantime, we construct an invariant Kahler metric, which is complete and not less than Bergman metric, such that its holomorphic sectional curvature is bounded above by a negative constant. Hence we obtain the comparison theorem for the Bergman and Kobayashi metrics on E(m, n, K).

ISSN:0278-1077    

DOI:10.1080/17476939708815059

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

This paper deals with the Riemann-Hilbert boundary value problem for nonlinear elliptic complex equations ofnorder in simply and multiply connected domains. Firstly we give the formulation of the Riemann-Hilbert problem and its well posedness and then we give the representation of solutions for the modified boundary value problem and prove its solvability, and finally derive solvability conditions of the original Kiemaiin-Hilbert problem. In the following, we divide into two cases of complex equations of2nth order and2n+ 1th order to discuss.

ISSN:0278-1077    

DOI:10.1080/17476939708815060

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

The paper proves that for two arbitrary transcendental entire functionsf(z)andg(z)and a non-constant polynomialP(z)there exists a setIhaving logarithmic density one such that

ISSN:0278-1077    

DOI:10.1080/17476939708815061

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

In his monograph [11] Walsh considers approximation to analytic functions on compact sets by interpolation with rational functions with prescribed poles, and in two papers [3], [4] Bagby has in some sense completed the convergence theory by Walsh. The purpose of this paper is to study the interpolation problem in the general case and from a somewhat different point of view. We also give some concrete examples introducing the subject in an easy way.

ISSN:0278-1077    

DOI:10.1080/17476939708815062

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We obtain the following result Letw(z) be a v-valued transcendental entire algebroid function and setThen if n0≥4v−2+2(v−1)(n1−1), we have for eace,wherep:=n0−4v+3−2(v−1)(n1−1)≥1.

ISSN:0278-1077    

DOI:10.1080/17476939708815063

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

This paper studies the problem of uniqueness of meromorphic functions whose n-th derivatives share the same 1-points. The results improve some theorems given by M. Ozawa, K. Shibazaki. X. H. Hua. C. C. Yang. H. X. Yi.K. L. Hiong and other authors. The examples are provided to show that some results in this paper are sharp.

ISSN:0278-1077    

DOI:10.1080/17476939708815064

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We derive weighted noun inequalities forMharmonic conjugate functions on higher dimension.

ISSN:0278-1077    

DOI:10.1080/17476939708815065

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor

摘要:

We study the boundary correspondence under quasiconformal self-mappings. in the plane and in space. First, considering quasiconformal mappingsfof the upper half-plane onto itself, we give new sufficient conditions for the boundary correspondence λ↱f(λ) to be aC1-homeomorphism. Then for quasicontormal self-mappingsfof the upper half-spaceHnn≥ 3. we show that both of the well-known Carleson conditions as well as the condition of the approximate continuity for the distortion coefficientKfn:(x) imply that is a similarity mapping. The proofs are based on a regularity theorem due to Tciehmüller. Wittich, Belinskii and Lehto in the plane and similar results due to Reshetnyak in space.

ISSN:0278-1077    

DOI:10.1080/17476939708815066

出版商:Gordon and Breach Science Publishers    

年代:1997

数据来源: Taylor