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

We give a characterization of the extremal sequences for the Bellman function of three variables of the dyadic maximal operator in relation to Kolmogorov's inequality. In fact we prove that they behave approximately like eigenfunctions of this operator for a specific eigenvalue. For this approach we use the one introduced in a paper by A. D. Melas and the author, where the respective Bellman function has been precisely evaluated.