Boundary values of Cauchy type integrals
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V. V. Kapustin
Translated by: the author - St. Petersburg Math. J. 16 (2005), 691-702
- DOI: https://doi.org/10.1090/S1061-0022-05-00873-3
- Published electronically: June 23, 2005
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Abstract:
Results by A. G. Poltoratskiĭ and A. B. Aleksandrov about nontangential boundary values of pseudocontinuable $H^2$-functions on sets of zero Lebesgue measure are used for the study of operators on $L^2$-spaces on the unit circle. For an arbitrary bounded operator $X$ acting from one such $L^2$-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 $X$ 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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Bibliographic 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
- Received by editor(s): January 20, 2004
- Published electronically: June 23, 2005
- Additional Notes: Partially supported by RFBR (grant no. 02–01–00264), and by the SS grant no. 2266.2003.1.
- © Copyright 2005 American Mathematical Society
- Journal: St. Petersburg Math. J. 16 (2005), 691-702
- MSC (2000): Primary 30E20, 47B47
- DOI: https://doi.org/10.1090/S1061-0022-05-00873-3
- MathSciNet review: 2090853