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Functions with unbounded ∂-derivative and their boundary functions

Part of: Geometric function theory

Published online by Cambridge University Press:  09 April 2009

Chen Zhiguo ,
Chen Jixiu  and
He Chengqi
Chen Zhiguo
Affiliation:
Institute of Mathematics and Department of Mathematics Fudan University Shanghai, 200433 P. R., China
Chen Jixiu
Affiliation:
Institute of Mathematics and Department of Mathematics Fudan University Shanghai, 200433 P. R., China
He Chengqi
Affiliation:
Institute of Mathematics and Department of Mathematics Fudan University Shanghai, 200433 P. R., China
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Abstract

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Let F(z) be a continuous complex-valued function defined on the closed upper half plane H whose generalized derivative ∂F(z) is unbounded. In this paper, we discuss the relationship between the increasing order of ]∂F(x + iy)] when y → 0 and that of λf(x, t) ](F(x + t) − 2F(x) + F(x − t))/t], (x, t ∈ R), when t → 0.

MSC classification

Secondary: 30C62: Quasiconformal mappings in the plane
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 1 , August 1997 , pp. 100 - 109
Copyright
Copyright © Australian Mathematical Society 1997

References

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