Best Uniform Approximation by Bounded Analytic Functions

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1988Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 103, page 882 (issn: 0002-9939,

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Authors: Papadimitrakis, M.;

doi: 10.2307/2046869 , 10.1090/s0002-9939-1988-0947674-9

Best Uniform Approximation by Bounded Analytic Functions

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Abstract

This paper gives a counterexample to the conjecture that the continuity of the conjugate f ~ \tilde f of an f ∈ C ( T ) f \in C\left ( T \right ) implies the continuity of the best uniform approximation g ∈ H ∞ ( T ) g \in {H^\infty }\left ( T \right ) of f f . It also states two conditions which imply the continuity of g g .

Keywords

Conjugate functions, conjugate series, singular integrals, conjugate function, best uniform approximation, \(H^p\)-classes

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