摘要:

LetBdenote a proper open subset of. In a recent paper we have defined holomorphic functions in tubeswhich generalize the HardyHp(TB) spaces and have obtained representations of the functions in these new spaces in terms of Fourier—Laplace, Cauchy, and Poisson integrals for certain values ofpand for appropriate types of basesBof the tubeTB. In this paper we obtain a necessary and sufficient condition for an elementf(z) in our new spaces to be inHp{TC), 1 < p > ∞, whereCis a regular cone inthe condition is thatf(x + iy) obtain a functionh(x) ∈Lpas distributional boundary value in the strong topology of the tempered distributions as. In both directions the holomorphic functionf(z) can be recovered by the Poisson integral of the boundary valueh(x).

ISSN:0278-1077    

DOI:10.1080/17476938408814046

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

This article extends the Lehto majorant principle to a family of normalized quasiconformal mappingsfthat are analytic outsideDand whose complex dilatationsμlsatisfyinD. Bounds on several coefficients, an area theorem, and Grunsky inequalities are given. In addition a singular integral representation is used to analyse sharpness.

ISSN:0278-1077    

DOI:10.1080/17476938408814047

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Iffis a function of classLpon the torusand if the subsetEofis the peak set of a function of classAp(UN), then there is a functionginAp− l,α(UNfor allαbetween zero and one withg=fonE. The peak sets of functions of classAp(Un) lie in locally closed interpolation submanifolds of the torus of classLp. but an example shows that they need not lie in closed interpolation submanifolds.

ISSN:0278-1077    

DOI:10.1080/17476938408814048

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

LetRnandSmbe two algebroid surfaces defined byyn=G(z) andum=g(w), respectively. We here discuss the existence of analytic mappings ofRnintoSm. WhenRnandSm, especially, are regularly branched algebroid surfaces withP(Rn) = 2nandP(Sm) = 2m, respectively, we give a perfect condition for the existence of an analytic mapping ofRnintoSmand show a relation between two analytic mappings ofRnintoSn.

ISSN:0278-1077    

DOI:10.1080/17476938408814049

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Collingwood and Cartwright have shown an analogue in the small of Iversen's theorem which states that, in the neighborhood of an isolated essential singularity of a meromorphic function, an exceptional value is also an asymptotic value. It is called the main theorem in the small and states the relations between the cluster set, exceptional values and asymptotic values for a function meromorphic in the open unit disc. This note represents an extension of work of Collingwood and Cartwright for an analytic mapping from a hyperbolic Riemann surface into a Riemann surface.

ISSN:0278-1077    

DOI:10.1080/17476938408814050

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

A Lerch's theorem for analytic functionals with unbounded carrier is proved. As applications Carlson's theorem, Polya's theorem and a Phragmen-Lindelöf type theorem are obtained for entire functions of exponential type in the left halfplane and of type 1 with respect to proximate order 1 + (log logr)/(logr) in the right half plane.

ISSN:0278-1077    

DOI:10.1080/17476938408814051

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

LetDbe a simply connected bounded region in the plane. Let z0εD. LetFθdenote the conformal automorphism ofDwith. Let Θ be the set of θ ε (0, 2π) such thatFθhas a continuous extension to the closure ofD. This paper investigates geometric and prime end properties of ðDwhich can be inferred from properties of Θ.

ISSN:0278-1077    

DOI:10.1080/17476938408814052

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Ahlfors introduced the geodesic curvature-area method and used it to obtain sharp upper and lower bounds for the conformal radius of a simply connected region. The method has a striking resemblance to extremal length except that it is limited toC2-metrics. By employing a different technique, Minda extended the upper bound to SK(k) metrics—upper semicontinuous metrics with generalized curvature at most —k≤0. Later, Minda used the geodesic curvature-area method to obtain a sharp upper bound for the modulus of a doubly connected region. Here we extend the bound to the class of SK(λ) metrics by using the length-area method in conjunction with an isoperimetric inequality. There are strong analogies between this result and classical facts concerning quadratic differentials and logarithmic area.

ISSN:0278-1077    

DOI:10.1080/17476938408814053

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

A symmetrization offrelating to computing the Laplacian ofis discussed together with its relationship to the theory of Dirichlet Integral inequalities.

ISSN:0278-1077    

DOI:10.1080/17476938408814054

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

This paper is concerned with the system of ordinary linear differential equationswithA(Z) (n:)-matrix of meromorphic functions in a neighborhood of the (isolated) singular point 0 anda column vector of dimensionn. First we prove a new theorem about the reduction of such systems, by which a generally known result of J. Moser [12] from 1960 is essentially improved. With the help of a method from H. L. Turrittin [13], which was extended by us, this result finally leads to a lower bound for the reduction. Then according to our former result [7] this is also a lower bound for the maximum order ρmaxof a fundamental solution matrix: ρmax≥(1/n)δ(A). The quantity δ(A) is the limit of a sequence of quantities which characterize the singular behavior inz= 0. We will show that δ(A) is an invariant and that δ(A) = 0 holds if and only if the system is regular singular inz= 0. At the end of the paper the results will be applied to ordinary linear differential equations.

ISSN:0278-1077    

DOI:10.1080/17476938408814055

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor