This is an announcement for the paper "Rearrangements with supporting trees, isomorphisms and combinatorics of coloured dyadic intervals" by Anna Kamont and Paul F. X. Mueller.
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.
Archive classification: math.FA
Mathematics Subject Classification: 46B25; 46E40; 91A05
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Submitted from: pfxm@bayou.uni-linz.ac.at
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