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Complex-Harmonic Meier’s Theorem

Published online by Cambridge University Press:  22 January 2016

Shinji Yamashita
Shinji Yamashita*
Affiliation:
Mathematical Institute, Tôhoku University, Sendai 980, Japan
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1. Fatou’s theorem is true for a bounded complex-valued harmonic function in the disk D: |z|<1. One asks naturally: “Is Meier’s topological analogue of Fatou’s theorem (simply, “MF theorem”; [14, p. 330, Theorem 6], cf. [10, p. 154, Theorem 8.9]) true for a bounded complex-valued harmonic function in D?” We shall give the affirmative answer to this question. Furthermore, the horocyclic MF theorem [2, p. 14, Theorem 5] in the complex-harmonic form will be proved in parallel.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 43 , September 1971 , pp. 161 - 165
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

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