Geodesic
The Bellman functions for a certain two-weight inequality: A~case study
Algebra i analiz, Tome 18 (2006) no. 2, pp. 24-56.

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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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V. Vasyunin; A. Vol'berg. The Bellman functions for a certain two-weight inequality: A~case study. Algebra i analiz, Tome 18 (2006) no. 2, pp. 24-56. https://geodesic-test.mathdoc.fr/item/AA_2006_18_2_a1/

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