Journal of Mathematical Sciences

, Volume 182, Issue 5, pp 714–723 | Cite as

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


We prove the following corrections theorem: Any function f on the circle \( {\mathbb T} \) that is bounded by an α 1-weight w (which means that \( M{w^2} \leqslant C{w^2} \)) can be modified on a set with \( \mathop \smallint \limits_e w \leqslant \varepsilon \) so that its quadratic function built up from an arbitrary sequence of nonintersecting intervals in ℤ will not exceed \( C\log \frac{1}{\varepsilon }w \). Bibliography: 11 titles.


Quadratic Function Arbitrary Sequence Correction Theorem Nonintersecting Interval 
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© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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