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

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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.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    D. M. Stolyarov

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  1. D. M. Stolyarov
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Correspondence to D. M. Stolyarov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 389, 2011, pp. 232–251.

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Stolyarov, D.M. New correction theorems in the light of a weighted Littlewood-Paley-Rubio de Francia inequality. J Math Sci 182, 714–723 (2012). https://doi.org/10.1007/s10958-012-0775-6

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  • DOI: https://doi.org/10.1007/s10958-012-0775-6

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