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1 results

  • Rearrangementsof the Haar system that preserve BMO

  • PFX Müller
  • Journal:
    Proceedings of the London Mathematical Society / Volume 75 / Issue 3 / November 1997
    Published online by Cambridge University Press:
    01 November 1997, pp. 600-618
    Print publication:
    November 1997

  • Let $\cal D $ denote the collection of dyadicintervals in the unit interval. Let $\tau$ be a rearrangement of the dyadic intervals. We study theinduced operator

    $$ Th_I = h_{\tau(I)}$$

    where $h_I$ is the $L^{\infty}$ normalizedHaar function. We find geometric conditions on $\tau$ which are necessary and sufficient for $T$ to bebounded on $BMO$. We also characterize the rearrangements of the $L^p$ normalized Haar system in$L^p.$

    1991 Mathematics Subject Classification: 42C20, 43A17, 47B38.