Unconditionality of general Franklin systems in $L^p[0,1]$, $1< p< \infty $
Volume 164 / 2004
Studia Mathematica 164 (2004), 161-204
MSC: 42C10, 46E30.
DOI: 10.4064/sm164-2-4
Abstract
By a general Franklin system corresponding to a dense sequence ${\cal T}=(t_n, n \geq 0)$ of points in $[0,1]$ we mean a sequence of orthonormal piecewise linear functions with knots ${\cal T}$, that is, the $n$th function of the system has knots $t_0, \ldots, t_n$. The main result of this paper is that each general Franklin system is an unconditional basis in $L^p[0,1]$, $1< p< \infty$.
