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

2009/09/28 by Anna Kamont, Kamont, Anna, Paul F. X. Mueller +1 · 1 citation
Mathematics · #46B25 #46E40 #91A05 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B25 #msc:46E40 #msc:91A05

paper · pdf · doi:10.48550/arxiv.0909.4926

arxiv created 2009/09/28 · arxiv updated 2009/12/01

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.

Cited by

• Combinatorics of Dyadic Intervals: Consistent Colorings

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