New correction theorems in the light of a weighted Littlewood--Paley--Rubio de Francia inequality

D. M. Stolyarov

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 $M{w}^2\le C{w}^2$) can be m…