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Necessary and sufficient conditions for the $L^{1}$ -convergence of double Fourier series

Péter Kórus (2018)

Czechoslovak Mathematical Journal

We extend the results of paper of F. Móricz (2010), where necessary conditions were given for the $L^{1}$ -convergence of double Fourier series. We also give necessary and sufficient conditions for the $L^{1}$ -convergence under appropriate assumptions.

Necessary conditions for the $L^{p}$ -convergence $(0 < p < 1)$ of single and double trigonometric series

Xhevat Z. Krasniqi, Péter Kórus, Ferenc Móricz (2014)

Mathematica Bohemica

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. 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 $0 < p < 1$ .

Nonlinear Approximation by Trigonometric Sums.

R.A. DeVore, V.N. Temlyakov (1995)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Number of real roots of a random trigonometric polynomial.

Farahmand, K. (1992)

Journal of Applied Mathematics and Stochastic Analysis

Displaying 1 – 4 of 4

Necessary and sufficient conditions for the L 1 -convergence of double Fourier series

Necessary conditions for the L p -convergence ( 0 < p < 1 ) of single and double trigonometric series

Nonlinear Approximation by Trigonometric Sums.

Number of real roots of a random trigonometric polynomial.

Currently displaying 1 – 4 of 4

Necessary and sufficient conditions for the $L^{1}$ -convergence of double Fourier series

Necessary conditions for the $L^{p}$ -convergence $(0 < p < 1)$ of single and double trigonometric series