Xhevat Z. Krasniqi, University of Prishtina, Department of Mathematics and Computer Sciences, Avenue Mother Theresa 5, Prishtinë, 10000, Kosovë, e-mail: xheki00@hotmail.com; Péter Kórus (corresponding author), Ferenc Móricz, University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, Szeged, 6720 Hungary, e-mail: korpet@math.u-szeged.hu, moricz@math.u-szeged.hu
Abstract: We give necessary conditions in terms of the coefficients for the convergence of a double trigonometric series in the $L^p$-metric, where $0<p<1$. The results and their proofs have been motivated by the recent papers of A. S. Belov (2008) and F. Moricz (2010). Our basic tools in the proofs are the Hardy-Littlewood inequality for functions in $H^p$ and the Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials and their conjugates in the $L^p$-metric, where $0<p<1$.
Keywords: trigonometric series; Hardy-Littlewood inequality for functions in $H^p$; Bernstein-Zygmund inequalities for the derivative of trigonometric polynomials in $L^p$-metric for $0<p<1$; necessary conditions for the convergence in $L^p$-metric
Classification (MSC 2010): 42A16, 42A20, 42B05, 42B30, 42B99
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