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Closure of analytic polynomials in weighted Jordan curves. (English) Zbl 0588.42014

PolynĂ´mes orthogonaux et applications, Proc. Laguerre Symp., Bar-le- Duc/France 1984, Lect. Notes Math. 1171, 204-210 (1985).
[For the entire collection see Zbl 0572.00007.]
The authors consider a theory of \(H^ p(\Gamma,\mu)\) spaces, \(0<p<\infty\), where \(\Gamma\) is a rectifiable Jordan curve and \(d\mu\) is a finite nonnegative measure on \(\Gamma\) which is absolutely continuous with respect to arc length. It is further assumed that the region inside \(\Gamma\) is a Smirnov domain. The results presented include a comparison between \(H^ p(\Gamma d\mu)\) and \(L^ p(\Gamma,\mu)\), duality, and study of the conjugation operator.
Reviewer: M.Milman

MSC:

42B30 \(H^p\)-spaces

Citations:

Zbl 0572.00007