Convergence in norm of logarithmic means of multiple Fourier series

DOI10.7153/MIA-18-62zbMATH Open1321.42016arXiv1310.8209OpenAlexW2516170899MaRDI QIDQ2944180

L. D. Gogoladze, Ushangi Goginava

Publication date: 28 August 2015

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Abstract: The maximal Orlicz space such that the mixed logarithmic means of multiple Fourier series for the functions from this space converge in $L_1$-norm is found.

Full work available at URL: https://arxiv.org/abs/1310.8209

zbMATH Keywords

Orlicz spacesmultiple Fourier seriesNörlund logarithmic meansRiesz logarithmic means

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Cesàro, Euler, Nörlund and Hausdorff methods (40G05) Fourier series and coefficients in several variables (42B05) Summability in several variables (42B08)

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