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arXiv · 0909.4926

Rearrangements with supporting Trees, Isomorphisms and Combinatorics of coloured dyadic Intervals

Anna Kamont·Paul F. X. Mueller
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Abstract

We determine a class of rearrangements that admit a supporting tree. This condition implies that the associated rearrangement operator has a bounded vector valued extension. We show that there exists a large subspace of $L^p$ on which a bounded rearrangement operator acts as an isomorphism. The combinatorial issues of these problems give rise to a two-person game, to be played with colored dyadic intervals. We determine winning strategies for each of the players.

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Anna Kamont, Paul F. X. Mueller. 2009-09-28. Rearrangements with supporting Trees, Isomorphisms and Combinatorics of coloured dyadic Intervals. https://arxiv.org/abs/0909.4926

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