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Permutations of the Haar system

Paul F. X. Müller
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Abstract

General permutations acting on the Haar system are investigated. We give a necessary and sufficient condition for permutations to induce an isomorphism on dyadic BMO. Extensions of this characterization to Lipschitz spaces $\lip, (0<p\leq1)$ are obtained. When specialized to permutations which act on one level of the Haar system only, our approach leads to a short straightforward proof of a result due to E.M.Semyonov and B.Stoeckert.

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Paul F. X. Müller. 1990-06-25. Permutations of the Haar system. https://arxiv.org/abs/math/9201213

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