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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 $0 < p < 1$ .

Displaying 1 – 4 of 4

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

Newer applications of generalized monotone sequences.

Note on differentiation of integrals and the halo conjecture

Note on the absolute convergence of Fourier series of a function of Wiener’s class $V_{r}$

Currently displaying 1 – 4 of 4

Displaying 1 – 4 of 4

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

Newer applications of generalized monotone sequences.

Note on differentiation of integrals and the halo conjecture

Note on the absolute convergence of Fourier series of a function of Wiener’s class V r

Currently displaying 1 – 4 of 4

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

Note on the absolute convergence of Fourier series of a function of Wiener’s class $V_{r}$