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On the extension of a theorem of Stein and Weiss and its application
Authors:
Ivan H. Feschiev ab;
Snezhana G. Gocheva-Ilieva ab
| Affiliations: | a Faculty of Mathematics and Informatics, Plovdiv University “Paisii Hilendarski”, Plovdiv, Bulgaria |
| b Communicated by D-C Chang, |
DOI:
10.1080/02781070410001731684
Publication Frequency:
12 issues per year
Published in:
Complex Variables and Elliptic Equations,
Volume
49,
Issue
10
August
2004
, pages 711
- 730
Complex Variables and Elliptic Equations,
Volume
49,
Issue
10
August
2004
, pages 711
- 730
Subjects:
Analysis - Mathematics;
Complex Variables;
Computational Numerical Analysis;
Functional Analysis;
Mathematical Analysis;
Theory of Numbers;
Number of References: 6
Formats available:
HTML
(English)
:
PDF
(English)
Previously published as:
Complex Variables, Theory and Application: An International Journal
(0278-1077,
1563-5066)
until 2006
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Abstract
In this paper there is proved a generalization of a theorem of Stein and Weiss concerning metric properties of the conjugate characteristic functions of given sets on the interval [0, 2π]. As an application for the Hilbert transform of a bounded function, the optimal correlation
 where the Favard's constant  :  is also established.
|
| Keywords: Fourier series; Conjugate characteristic functions; Lebesgue's measure; Optimal correlation; Upper estimation; 1991 Mathematics Subject Classification: Primary 42A50; Secondary 28A25 |
| view references (6) |
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