Abstract
We show how the Bellman function method can be used to obtain sharp inequalities for the maximal operator of a dyadic A 1 weight on \({\mathbb{R}^n}\) . Using this approach, we determine the optimal constants in the corresponding weak-type estimates. Furthermore, we provide an alternative, simpler proof of the related maximal L p-inequalities, originally shown by Melas.
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Research supported by the NCN Grant DEC-2012/05/B/ST1/00412.
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Osȩkowski, A. Sharp inequalities for dyadic A 1 weights. Arch. Math. 101, 181–190 (2013). https://doi.org/10.1007/s00013-013-0537-9
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DOI: https://doi.org/10.1007/s00013-013-0537-9