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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

The Bellman functions for a certain two-weight inequality: A case study


Authors: V. Vasyunin and A. Volberg
Translated by: the authors
Original publication: Algebra i Analiz, tom 18 (2006), nomer 2.
Journal: St. Petersburg Math. J. 18 (2007), 201-222
MSC (2000): Primary 42B20, 42A50, 47B35
Published electronically: March 20, 2007
MathSciNet review: 2244935
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Abstract | References | Similar Articles | Additional Information

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.


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Additional 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

DOI: http://dx.doi.org/10.1090/S1061-0022-07-00953-3
PII: S 1061-0022(07)00953-3
Keywords: Bellman function, Sawyer test, two-weight estimate
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).
Article copyright: © Copyright 2007 American Mathematical Society