On the non-equivalence of rearranged Walsh and trigonometric systems in $L_p$
Volume 159 / 2003
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.
