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Mathematics. Mechanics. Informatics

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Fadeev A. A., Volosivets S. S. Weighted Integrability of Sums of Series with Respect to Multiplicative Systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 2, pp. 129-136. DOI: 10.18500/1816-9791-2014-14-2-129-136

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Weighted Integrability of Sums of Series with Respect to Multiplicative Systems

Fadeev Aleksandr Andreevich, Saratov State University
Volosivets Sergei Sergeevich, Saratov State University

A necessary and sufficient condition for Lp-integrability with power weight of a function f represented by the series with respect to multiplicative systems with generalized monotone coefficients is obtained. The integrability of the majorant of partial sums of a representing series is also described by the same conditions. In addition we study the integrability of difference quotient (f(x) − f(0))/x.

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