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Asymptotic Values and Minimal Fine Limits of Subharmonic Functions of Slow Growth
Author(s) -
Gardiner Stephen J.
Publication year - 1998
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610798006176
Subject(s) - subharmonic , harmonic function , harmonic measure , boundary (topology) , mathematical analysis , mathematics , measure (data warehouse) , subharmonic function , limit (mathematics) , harmonic , boundary values , function (biology) , boundary value problem , space (punctuation) , pure mathematics , physics , nonlinear system , computer science , quantum mechanics , database , evolutionary biology , biology , operating system
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.