The Bellman functions for a certain two-weight inequality: A case study
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V. Vasyunin and A. Volberg
Translated by: the authors - St. Petersburg Math. J. 18 (2007), 201-222
- DOI: https://doi.org/10.1090/S1061-0022-07-00953-3
- Published electronically: March 20, 2007
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Abstract:
A formula is presented for the exact Bellman function of a certain “toy” two-weight problem. This adds one more function to a short list of other Bellman functions for which the precise expressions have recently been found. The case study reveals essential features of finding Bellman functions in general and gives the extremal sequences for the problem. Some open questions are posed.References
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Bibliographic Information
- V. Vasyunin
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
- Email: vasyunin@pdmi.ras.ru
- A. Volberg
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
- Email: volberg@yandex.ru
- Received by editor(s): November 30, 2005
- Published electronically: March 20, 2007
- Additional Notes: The first author was partially supported by RFBR (grant no. 05-01-00925).
The second author was partially supported by NSF (grant DMS 0200713). - © Copyright 2007 American Mathematical Society
- Journal: St. Petersburg Math. J. 18 (2007), 201-222
- MSC (2000): Primary 42B20, 42A50, 47B35
- DOI: https://doi.org/10.1090/S1061-0022-07-00953-3
- MathSciNet review: 2244935