Proceedings of the American Mathematical Society

Author(s): Evgueni Doubtsov
Journal: Proc. Amer. Math. Soc. 126 (1998), 515-522.
MSC (1991): Primary 30D50; Secondary 30D55
Retrieve article in: PDF
This article is available free of charge

Abstract: Given $0<p<2$

and a strictly positive continuous function $\varphi$ on the unit circle, we construct a bounded analytic function $g$

such that $|g^{*}|=\varphi$ a.e., and $g$

is in the Besov space $A_{p}^{1}$ on the unit disc.

1.: A. B. Aleksandrov, The existence of inner functions in the ball, Mat. Sb. 118 (160), no. 2 (6) (1982), 147-163; English transl., Math. USSR-Sb. 46 (1983), 143-159. (Russian) MR 83i:32002
2.: Y. Dupain, Gradients des fonctions intérieures dans la boule unité de ${\mathbb C\,}^{n}$ , Math. Z. 193 (1986), 85-94. MR 87j:32006
3.: J. Garnett, Bounded analytic functions, Academic Press, New York, 1981. MR 83g:30037
4.: S. V. Hruscev and V. V. Peller, Hankel operators, best approximations, and stationary Gaussian processes, Uspekhi Mat. Nauk 37, no. 1 (1982), 53-124; English transl., Russian Math. Surveys 37 (1982), 61-144. (Russian)
5.: S. N. Mergelyan, On one integral for analytic functions, Izvestiya Akad. Nauk SSSR 15 (1951), 395-400 (Russian). MR 13:335f
6.: W. Rudin, The radial variation of analytic functions, Duke Math. J. 22 (1955), 235-242. MR 18:27g
7.: -, Function Theory in the Unit Ball of ${\mathbb C\,}^{n}$ , Grundlehren Math. Wiss., vol. 241, Springer, Berlin, 1980. MR 82i:32002
8.: S. A. Vinogradov, Multiplication and division in the space of analytic functions with area integrable derivative, and in some related spaces, Zap. Nauchn. Sem. S. Petersburg. Otdel. Mat. Inst. Steklov. (POMI) 222 (1995), 45-77 (Russian); English transl. in J. Math. Sci.

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30D50, 30D55

Evgueni Doubtsov
Affiliation: Centre de Recerca Matemàtica, Institut d'Estudis Catalans, Apartat 50, E-08193 Bellaterra, Barcelona, Spain
Address at time of publication: ul. Partizana Germana 14/117, kv. 335, 198205 St. Petersburg, Russia
Email: doubtsov@crm.es, es@dub.pdmi.ras.ru

DOI: 10.1090/S0002-9939-98-04054-4
PII: S 0002-9939(98)04054-4
Keywords: Hardy classes, Besov space, inner-outer factorization
Received by editor(s): March 13, 1996
Received by editor(s) in revised form: August 13, 1996
Additional Notes: Supported by the Centre de Recerca Matemàtica, Institut d'Estudis Catalans (Barcelona) under a grant from DGICYT (Spain).
Communicated by: Albert Baernstein II
Copyright of article: Copyright 1998, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS