Abstract
We extend the results of Rubio de Francia and Bourgain by showing that, for arbitrary mutually disjoint intervals Δk ⊂ ℤ+, arbitrary p ∈, (0, 2], and arbitrary trigonometric polynomials f k with supp \(\hat f_k \subset \Delta _k \), we have
. The method is a development of that by Rubio de Francia. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 327, 2005, pp. 98–114.
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Kislyakov, S.V., Parilov, D.V. On the Littlewood-Paley theorem for arbitrary intervals. J Math Sci 139, 6417–6424 (2006). https://doi.org/10.1007/s10958-006-0359-4
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DOI: https://doi.org/10.1007/s10958-006-0359-4