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

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

2011-05-31

arxiv.org/abs/1105.6215v1

Mathematics

Functional Analysis

Scientific paper

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 $C \log \frac{1}{\eps} w$.

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