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We give a characterization of the extremal sequences for the Bellman functionof three variables of the dyadic maximal operator in relation to Kolmogorov'sinequality. In fact we prove that they behave approximately like eigenfunctionsof this operator for a specific eigenvalue. For this approach we use the oneintroduced in [4], where the respective Bellman function has been preciselyevaluated.

Extremal sequences for the Bellman function of three variables of the dyadic maximal operator in relation to Kolmogorov's inequality