From the class of Dirichlet finite harmonic functions we proceed to other classes of harmonic functions related to certain boundedness properties. Two central ones are boundedness in absolute value and positiveness. Two derived boundedness properties, quasiboundedness and essential positiveness, will also be considered. These fall into the general category of Φ-boundedness.


Riemann Surface Meromorphic Function Ideal Boundary Superharmonic Function Determine Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1970

Authors and Affiliations

  • L. Sario
    • 1
  • M. Nakai
    • 2
  1. 1.Unversity of CaliforniaCaliforniaUSA
  2. 2.Nagoya UnversityGermany

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