On Double Cosine, Sine, and Walsh Series with Monotone Coefficients

DOI10.2307/2048004zbMath0741.42010OpenAlexW4242910440MaRDI QIDQ4712674

Ferenc Móricz

Publication date: 25 June 1992

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2048004

zbMATH Keywords

pointwise convergencemonotone coefficientsdouble sine seriesdouble cosine seriesmaximum partial sumconvergence in \(L^ r\)-norm in Pringsheim sensetwo-dimensional Walsh series

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Fourier series and coefficients in several variables (42B05) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (14)

Weighted integrability of double series with respect to multiplicative systems ⋮ The Hardy-Littlewood theorem for multiple Fourier series with monotone coefficients ⋮ On weighted integrability of double cosine series ⋮ Convergence of trigonometric series with general monotone coefficients ⋮ Trigonometric series with general monotone coefficients ⋮ Two-dimensional Hardy-Littlewood theorem for functions with general monotone Fourier coefficients ⋮ Counterexamples to the Hardy-Littlewood theorem for generalized monotone sequences ⋮ Mean bounded variation condition and applications in double trigonometric series ⋮ Estimates of best approximations in integral metrics and Fourier coefficients with respect to multiplicative systems ⋮ Smoothness of sums of trigonometric series with monotone coefficients ⋮ A Hardy-Littlewood theorem for multiple series ⋮ On the classes \(\mathrm{H}_{p}^{\omega}\) and \(\mathrm{Lip} (\alpha, p)\) for trigonometric series with monotone coefficients ⋮ Hardy-Littlewood type inequalities for Vilenkin-Fourier coefficients ⋮ The Hardy-Littlewood theorem for double Fourier-Haar series from mixed metric Lebesgue \(L_{\bar p}[0, 1^2\) and net \(N_{\bar p,\bar q}(M)\) spaces]

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