Permutations of the Haar system
Paul F. X. Müller
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 , (0<p≤1) 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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