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On area integrals and radial variations of analytic functions in the unit disk

Published online by Cambridge University Press:  22 January 2016

Takafumi Murai
Takafumi Murai*
Affiliation:
Nagoya University
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We are concerned with the behaviour of analytic functions near the boundary. Let T and D be the unit circle |z| = 1 and the unit disk |z| < 1, respectively. The element of T is denoted by θ (0 ≤ θ < 2π). Let be analytic in D. The area integral A(f, θ) of f at θ is defined by

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 61 , July 1976 , pp. 135 - 159
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

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[3] Offord, A. C.; Distribution of values of random function in the unit disk, Studia Math., (1972), p. 71–106.CrossRefGoogle Scholar
[4] Zygmund, A.; Trigonometric series II, Cambridge, 1959.Google Scholar