%0 Journal Article
%T New correction theorems in the light of a weighted Littlewood--Paley--Rubio de Francia inequality
%A D. M. Stolyarov
%J Mathematics
%D 2011
%I arXiv
%X We prove the following correction theorem: every function $f$ on the circumference $\mathbb{T}$ that is bounded by the $\alpha_1$-weight $w$ (this means that $Mw^2 \leq C w^2$) can be modified on a set $e$ with $\int\limits_{e} w \leq \eps$ so that its quadratic function built up from arbitary sequence of nonintersecting intervals in $\mathbb{Z}$ will not exceed $C \log \frac{1}{\eps} w$.
%U http://arxiv.org/abs/1105.6215v1