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Majorant estimates for partial sums of multiple fourier series of functions from Orlicz spaces vanishing on some set

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Abstract

In this paper majorants supn |S n (x; ϕ)| of partial sums of double trigonometric Fourier series of functions fromL(log+ L)3 vanishing on some subsets ofT 2=[−π, π)2 are considered. In particular, the following theorem is proved.

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Authors and Affiliations

  1. Moscow State Technology University Stankin, Moscow, USSR

    O. K. Ivanova

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  1. O. K. Ivanova
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Translated fromMatematicheskie Zametki, Vol. 65, No. 6, pp. 821–830, June, 1999.

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Ivanova, O.K. Majorant estimates for partial sums of multiple fourier series of functions from Orlicz spaces vanishing on some set. Math Notes 65, 694–700 (1999). https://doi.org/10.1007/BF02675583

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  • DOI: https://doi.org/10.1007/BF02675583

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