By a general Franklin system corresponding to a dense sequence = (tₙ, n ≥ 0) of points in [0,1] we mean a sequence of orthonormal piecewise linear functions with knots , that is, the nth function of the system has knots t₀, ..., tₙ. The main result of this paper is that each general Franklin system is an unconditional basis in , 1 < p < ∞.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-2-4,
author = {Gegham G. Gevorkyan and Anna Kamont},
title = {Unconditionality of general Franklin systems in $L^{p}[0,1]$, 1 < p < $\infty$},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {161-204},
zbl = {1056.42022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-2-4}
}
Gegham G. Gevorkyan; Anna Kamont. Unconditionality of general Franklin systems in $L^{p}[0,1]$, 1 < p < ∞. Studia Mathematica, Tome 162 (2004) pp. 161-204. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-2-4/