BMO-estimation and almost everywhere exponential summability of quadratic partial sums of double Fourier series

DOI10.1007/s00365-014-9234-6zbMath1316.42013arXiv1303.0364OpenAlexW2125096305MaRDI QIDQ485329

Ushangi Goginava, L. D. Gogoladze, Grigori A. Karagulyan

Publication date: 9 January 2015

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0364

zbMATH Keywords

double Fourier seriesalmost everywhere convergenceBMO spacesstrong summabilityexponential meansquadratic partial sums

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Cesàro, Euler, Nörlund and Hausdorff methods (40G05) Fourier series and coefficients in several variables (42B05) Summability in several variables (42B08) Absolute and strong summability (40F05) Special methods of summability (40G99)

Related Items (10)

Strong summability of double Vilenkin–Fourier series ⋮ Strong approximation by Marcinkiewicz means of twodimensional Walsh-Kaczmarz-Fourier series ⋮ Two-dimensional martingale transforms and their applications in summability of Walsh-Fourier series ⋮ Almost everywhere strong \(C,1,0\) summability of 2-dimensional trigonometric Fourier series ⋮ Almost everywhere convergence of strong Nörlund logarithmic means of Walsh-Fourier series ⋮ On exponential summability of rectangular partial sums of double trigonometric Fourier series ⋮ Marcinkiewicz summability of Fourier series, Lebesgue points and strong summability ⋮ An exponential estimate for the cubic partial sums of multiple Fourier series ⋮ Almost everywhere strong summability of Fejér means of rectangular partial sums of two-dimensional Walsh-Fourier series ⋮ Strong summability of two-dimensional Vilenkin-Fourier series

Cites Work

• Strong approximation by Marcinkiewicz means of two-dimensional Walsh-Fourier series
• The space BMO and strong means of Fourier series
• Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series
• Everywhere divergent \(\Phi\)-means of Fourier series
• The weak type inequality for the maximal operator of the Marcinkiewicz-Fejér means of the two-dimensional Walsh-Fourier series
• Summation of multiple Fourier series in multiplicative systems
• On divergence of a subsequence of the partial sums of multiple trigonometric Fourier series
• Convergence almost everywhere of certain singular integrals and multiple Fourier series
• On the strong approximation of Fourier series
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