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Behavior of the constant in Korenblum's maximum principle
Author(s) -
Wang Chunije
Publication year - 2008
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200510616
Subject(s) - mathematics , constant (computer programming) , annulus (botany) , unit (ring theory) , unit disk , space (punctuation) , plane (geometry) , combinatorics , maximum principle , mathematical analysis , mathematical physics , geometry , philosophy , mathematics education , computer science , programming language , mathematical optimization , linguistics , botany , optimal control , biology
Let A p () ( p ≥ 1) be the Bergman space over the open unit disk in the complex plane. Korenblum's maximum principle states that there is an absolute constant c ∈ (0, 1) (may depend on p ), such that whenever | f ( z )| ≤ | g ( z )| ( f , g ∈ A p ()) in the annulus c < | z | < 1, then ∥ f A p≤ ∥ g ∥ A p. For p ≥ 1, let c p be the largest value of c for which Korenblum's maximum principle holds. In this note we prove that c p → 1 as p → ∞. Thus we give a positive answer of a question of Hinkkanen. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)