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Boundary values of Cauchy type integrals
Author(s):
V.
V.
Kapustin
Translated by:
the author
Original publication:
Algebra i Analiz,
tom 16
(2004),
vypusk 4.
Journal:
St. Petersburg Math. J.
16
(2005),
691-702.
MSC (2000):
Primary 30E20, 47B47
Posted:
June 23, 2005
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Additional information
Abstract:
Results by A. G. Poltoratskii and A. B. Aleksandrov about nontangential boundary values of pseudocontinuable  -functions on sets of zero Lebesgue measure are used for the study of operators on  -spaces on the unit circle. For an arbitrary bounded operator  acting from one such  -space to another and having the property that the commutator of it with multiplication by the independent variable is a rank one operator, it is shown that  can be represented as a sum of multiplication by a function and a Cauchy transformation in the sense of angular boundary values.
References:
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- 2.
- A. B. Aleksandrov, On the existence of nontangential boundary values of pseudocontinuable functions, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 222 (1995), 5-17; English transl., J. Math. Sci. 87 (1997), no. 5, 3781-3787. MR 1359992 (97a:30046)
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Additional Information:
V.
V.
Kapustin
Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email:
kapustin@pdmi.ras.ru
DOI:
10.1090/S1061-0022-05-00873-3
PII:
S 1061-0022(05)00873-3
Keywords:
Cauchy type integral,
angular boundary values,
intertwining relations
Received by editor(s):
20/JAN/2004
Posted:
June 23, 2005
Additional Notes:
Partially supported by RFBR (grant no. 02--01--00264), and by the SS grant no. 2266.2003.1.
Copyright of article:
Copyright
2005,
American Mathematical Society
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