A+ CATEGORY SCIENTIFIC UNIT

On the non-equivalence of rearranged Walsh and trigonometric systems in $L_p$

Volume 159 / 2003

Aicke Hinrichs, Jörg Wenzel Studia Mathematica 159 (2003), 435-451 MSC: 42C10, 42C20, 46B15. DOI: 10.4064/sm159-3-7

Abstract

We consider the question of whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in $L_p$ for some $p\not =2$. We show that this question is closely related to a combinatorial problem. This enables us to prove non-equivalence for a number of rearrangements. Previously this was known for the Walsh–Paley order only.

Authors

  • Aicke HinrichsMathematisches Institut
    FSU Jena
    D-07743 Jena, Germany
    e-mail
  • Jörg WenzelDepartment of Mathematics
    and Applied Mathematics
    University of Pretoria
    Pretoria 0002, South Africa
    e-mail

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