The BMO to BLO norm of the natural and classical dyadic maximal operators equals 1 for all n, via an explicit Bellman function on α-trees.
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The ${\rm BMO}\to{\rm BLO}$ action of the maximal operator on $\alpha$-trees
The BMO to BLO norm of the natural and classical dyadic maximal operators equals 1 for all n, via an explicit Bellman function on α-trees.