On Weyl multipliers of the rearranged trigonometric system

Abstract

We prove that the condition \begin{equation} \sum_{n=1}^\infty\frac{1}{nw(n)}<\infty \end{equation} is necessary for an increasing sequence of numbers $w(n)$ to be an almost everywhere unconditional convergence Weyl multiplier for the trigonometric system. This property for Haar, Walsh, Franklin and some other classical orthogonal systems was known long ago. The proof of this result is based on a new sharp logarithmic lower bound on $L^2$ of the majorant operator related to the rearranged trigonometric system.

31 pages

References in corpus (1)

• On systems of non-overlapping Haar polynomials

Cited by in corpus (1)

• On wavelet polynomials and Weyl multipliers