The sharp constant in the reverse Hölder inequality for Muckenhoupt weights
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V. Vasyunin
Translated by: the author - St. Petersburg Math. J. 15 (2004), 49-79
- DOI: https://doi.org/10.1090/S1061-0022-03-00802-1
- Published electronically: December 31, 2003
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Abstract:
Coifman and Fefferman proved that the “reverse Hölder inequality” is fulfilled for any weight satisfying the Muckenhoupt condition. In order to illustrate the power of the Bellman function technique, Nazarov, Volberg, and Treil showed (among other things) how this technique leads to the reverse Hölder inequality for the weights satisfying the dyadic Muckenhoupt condition on the real line. In this paper the proof of the reverse Hölder inequality with sharp constants is presented for the weights satisfying the usual (rather than dyadic) Muckenhoupt condition on the line. The results are a consequence of the calculation of the true Bellman function for the corresponding extremal problem.References
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Bibliographic Information
- V. Vasyunin
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191011, Russia
- Email: vasyunin@pdmi.ras.ru
- Received by editor(s): November 4, 2002
- Published electronically: December 31, 2003
- Additional Notes: Partially supported by RFBR (grant no. 02-01-00260a).
- © Copyright 2003 American Mathematical Society
- Journal: St. Petersburg Math. J. 15 (2004), 49-79
- MSC (2000): Primary 42B20, 42B25
- DOI: https://doi.org/10.1090/S1061-0022-03-00802-1
- MathSciNet review: 1979718