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A note on radial variation of analytic functions
Author(s) -
Hallenbeck D. J.,
Samotij K.
Publication year - 1991
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300006549
Subject(s) - mathematics , analytic function , class (philosophy) , unit disk , variation (astronomy) , unit (ring theory) , almost everywhere , pure mathematics , quasi analytic function , mathematical analysis , algebra over a field , non analytic smooth function , global analytic function , mathematics education , physics , artificial intelligence , astrophysics , computer science
Let F denote a family of analytic functions in the unit disk Δ. Suppose that one has a “sharp” estimate on the almost everywhere radial variation of functions in the class Δ. We prove that if Δ is contained in the Nevanlinna class N then the estimate will be “sharp” in the algebra A of functions analytic in Δ and continuous in Δ.