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

Vasyunin, V.; Volberg, A.

doi:10.1090/S1061-0022-07-00953-3

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

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