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On the Non-Equivalence of Rearranged Walsh and Trigonometric Systems in L_p

Aicke Hinrichs·Jörg Wenzel
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Abstract

We consider the question whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in L_p for some p<>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.

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Aicke Hinrichs, Jörg Wenzel. 2003-08-10. On the Non-Equivalence of Rearranged Walsh and Trigonometric Systems in L_p. https://arxiv.org/abs/math/0308091

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