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The weighted BMO condition and a constructive description of classes of analytic functions satisfying this condition. (English) Zbl 0849.30029

Georgian Math. J. 3, No. 3, 217-232 (1996); Corrigendum ibid. 3, No. 5, 500 (1996).
The author studies the problem of local polynomial approximation of holomorphic functions in domains with quasiconformal boundaries for weighted plane integral metrics. He presents a constructive description of a class of holomorphic functions satisfying a weak version of the BMO condition.
Reviewer: J.Siciak (Kraków)

MSC:

30E10 Approximation in the complex plane
41A10 Approximation by polynomials
30C62 Quasiconformal mappings in the complex plane
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References:

[1] L. N. Chikvinidze, Approximate functions in domains with quasiconformal boundary in weighted plane integral metrics.(Russian) Sibirskii Mat. J.XXX(1989),No. 2, 172–184;English translation: Siberian Math. J.30(1989),No. 2, 306–316.
[2] L. N. Chikvinidze, On approximation of functions in domains with quasiconformal boundary in weighted plane integral metrics.(Russian) Dokl. Akad. Nauk SSSR304(1989),No. 1, 41–43;English translation: Soviet. Math. Dokl.39(1989),No. 1, 32–34. · Zbl 0675.30028
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