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Integrability conditions for multiple trigonometric series

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Abstract

Sufficient conditions (the Boas-Telyakovskii conditions) on the coefficients of multiple trigonometric series are found that guarantee integrability of the sums of these series. Under these conditions, estimates are obtained for integrals of the moduli of the functions defined by multiple trigonometric series. In addition, the Boas-Telyakovskii conditions are compared with previously known conditions. It is shown that the Boas-Telyakovskii conditions are the most general ones.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of Ukraine, Kiev

    P. V. Zaderei

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  1. P. V. Zaderei
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 340–365, March, 1992.

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Zaderei, P.V. Integrability conditions for multiple trigonometric series. Ukr Math J 44, 297–317 (1992). https://doi.org/10.1007/BF01063131

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  • DOI: https://doi.org/10.1007/BF01063131

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