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MR2563741 (2011d:42046) 42B25
Melas, Antonios D.; Nikolidakis, Eleftherios Dyadic-like maximal operators on integrable functions and Bellman functions related to Kolmogorov's inequality. Trans. Amer. Math. Soc. 362 (2010), no. 3, 1571–1597.
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