Functions of bounded characteristic in n-connected domains. (English) Zbl 0719.30024
The paper extends to finitely connected domains results of J. H. Shapiro and A. L. Shields [Am. J. Math. 97(1975), 915-936 (1975; Zbl 0323.30033)] and J. W. Roberts [Illinois J. Math. 19, 553-559 (1975; Zbl 0313.30033)] concerning certain metric and topological properties of the Nevanlinna class N of functions of bounded characteristic in the unit disk. The techniques used is basically that of Robert and relies on the inner-outer factorization of class N in n- connected domains as suggested by R. Coifman and G. Weiss [Stud. Math. 23, 31-68 (1966; Zbl 0149.032)] and developed further by D. Khavinson [Pac. J. Math. 108, 295-318 (1983; Zbl 0494.30024); Mich. Math. J. 31, 371-379 (1984; Zbl 0592.30045)] and S. Ya. Khavinson [Usp. Mat. Nauk 44, No.4(268), 155-189 (1989; Zbl 0711.30041)]. The first 4 sections of the paper under review give an account of the combined results of Coifman and Weiss, and D. Khavinson with most proofs included. The main result of the article-extension to finitely connected domains of Roberts’ characterization of the connected component of the origin in class N is presented at the end of the final section 5.
Reviewer: D.Khavinson (Fayetteville)
MSC:
| 30D55 | \(H^p\)-classes (MSC2000) |
Citations:
Zbl 0521.30027; Zbl 0323.30033; Zbl 0313.30033; Zbl 0149.032; Zbl 0494.30024; Zbl 0592.30045; Zbl 0711.30041References:
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