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ASYMPTOTIC VALUES AND MINIMAL FINE LIMITS OF SUBHARMONIC FUNCTIONS OF SLOW GROWTH

Published online by Cambridge University Press:  01 June 1998

STEPHEN J. GARDINER
STEPHEN J. GARDINER
Affiliation:
Department of Mathematics, University College Dublin, Dublin 4, Ireland
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Abstract

This paper shows that a subharmonic function in the half-space which does not grow too rapidly near the boundary and which does not have asymptotic value +∞ at too many points must have finite minimal fine limits at a boundary set of positive measure. For harmonic functions, the conclusion may be expressed in terms of non-tangential limits. A related Phragmén–Lindelöf theorem is also established.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 668 - 676
Copyright
The London Mathematical Society 1998

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