The aim of this paper is to prove the following theorem of the PHRAGMEN-LINDE-LOF type. ## Theorem. Let f ( z ) be analytic in the angular domain and for some p E (0, + -) satistifis the following conditions: a) there exists the boundary function f [ r e q ) ( k i i x l ( 2 a ) ) I ~L p (0, +-) s
On the Lindelöf Theorem
✍ Scribed by F. W. Gehring; A. J. Lohwater
- Publisher
- John Wiley and Sons
- Year
- 1958
- Tongue
- English
- Weight
- 316 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0025-584X
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📜 SIMILAR VOLUMES
For an algebraic curve V in C k × C n it is investigated when it satisfies the Phragmén-Lindelöf condition PL(ω) of evolution in certain classes of ultradifferentiable functions. Necessary as well as sufficient conditions are obtained which lead to a complete characterization for curves in C × C n .
## Abstract Some new results of the PRAGMÉN‒LINDELÖF theory in 𝔜~+~ (namely the elementary method of successive mapping [4] and ROSSBERG's [8] non‒elementary theorem) are carried over to subharmonic functions. The theorems have – in spite of their very different nature – a common salient feature: R