On -Integrability of Multiple Trigonometric Series with General Monotone Coefficients
Mukanov A.B. Nursultanov E.D.
December 2025Pleiades Publishing
Proceedings of the Steklov Institute of Mathematics
2025#331Issue 1118 - 133 pp.
Abstract: We establish a criterion for the sum of a multiple (or one-dimensional) trigonometric series to belong to the Lebesgue space for and. We consider series whose coefficients satisfy a new general monotonicity condition, which does not reduce to any of the previously known forms of general monotonicity. In particular, we present examples of sequences that belong to this new class but are not contained in any of the previously studied classes of general monotone sequences. The results extend and refine the known criteria for the -integrability of the sums of multiple and one-dimensional trigonometric series.
general monotonicity , Lebesgue spaces , multiple series , trigonometric Fourier series
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Kazakhstan Branch of Lomonosov Moscow State University, Astana, Kazakhstan
LLP “Geometry”, Astana, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Kazakhstan Branch of Lomonosov Moscow State University
LLP “Geometry”
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