On the Non-Equivalence of Rearranged Walsh and Trigonometric Systems in Lp
Aicke Hinrichs, Jörg Wenzel
Abstract
We consider the question whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in Lp 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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