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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*
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
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

References

[1] Kahane, J. P.; Some random series of functions, Raytheon education company, 1968.Google Scholar
[2] Lohwater, A. J. and Piranian, G.; On a conjecture of Lusin, Michigan Math. J., (1955), p. 6368.Google Scholar
[3] Offord, A. C.; Distribution of values of random function in the unit disk, Studia Math., (1972), p. 71106.CrossRefGoogle Scholar
[4] Zygmund, A.; Trigonometric series II, Cambridge, 1959.Google Scholar