Geodesic
Necessary conditions for the $L^{p}$-convergence $(0$ of single and double trigonometric series
Mathematica Bohemica, Tome 139 (2014) no. 1, pp. 75-88

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We give necessary conditions in terms of the coefficients for the convergence of a double trigonometric series in the $L^{p}$-metric, where $0
We give necessary conditions in terms of the coefficients for the convergence of a double trigonometric series in the $L^{p}$-metric, where $0$. The results and their proofs have been motivated by the recent papers of A. S. Belov (2008) and F. Móricz (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 $0$.
DOI : 10.21136/MB.2014.143637
Classification : 42A16, 42A20, 42A32, 42B05, 42B30, 42B99
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 
Krasniqi, Xhevat Z.; Kórus, Péter; Móricz, Ferenc. Necessary conditions for the $L^{p}$-convergence $(0
  

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