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

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

2009-09-28

arxiv.org/abs/0909.4926v1

Mathematics

Functional Analysis

Scientific paper

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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