A necessary condition for uniform convergence of double sine series with $p$-bounded variation coefficients
Volume 166 / 2021
Colloquium Mathematicum 166 (2021), 291-312
MSC: 42A20, 42A32, 40A05, 40B05.
DOI: 10.4064/cm8419-3-2021
Published online: 27 September 2021
Abstract
We introduce a new class of double sequences called $DGM\left (p, \alpha ,\beta ,\gamma ,r\right )$, which is a generalization of a class considered by Duzinkiewicz and Szal (2018). We obtain a necessary condition for the uniform convergence of double sine series with coefficients belonging to this class.
