A Hardy-Littlewood theorem for multiple series

DOI10.1016/J.JMAA.2007.06.057zbMath1283.42031OpenAlexW2076274425MaRDI QIDQ2465161

M. I. D'yachenko, Sergey Yu. Tikhonov

Publication date: 8 January 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.06.057

zbMATH Keywords

Hardy-Littlewood theoremmultiple trigonometric seriesgeneral monotone coefficients

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25)

Related Items (12)

Weighted integrability of double series with respect to multiplicative systems ⋮ Hardy-Littlewood-Stein inequalities for double trigonometric series ⋮ The Hardy-Littlewood theorem for multiple Fourier series with monotone coefficients ⋮ Convergence of trigonometric series with general monotone coefficients ⋮ Two-dimensional Hardy-Littlewood theorem for functions with general monotone Fourier coefficients ⋮ Transformation of Fourier series by means of general monotone sequences ⋮ \(L^p(\mathbb R^n)\)-continuity of translation invariant anisotropic pseudodifferential operators: a necessary condition ⋮ Counterexamples to the Hardy-Littlewood theorem for generalized monotone sequences ⋮ Mean bounded variation condition and applications in double trigonometric series ⋮ On weighted integrability of double sine series ⋮ On summability of Fourier coefficients of functions from Lebesgue space ⋮ 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]

Cites Work

• Unnamed Item
• Unnamed Item
• On generalized Walsh Fourier series
• Trigonometric series with general monotone coefficients
• On the Hardy and Bellman transforms for orthogonal Fourier series.
• Exponential sums with coefficients 0 or 1 and concentrated \(L^p\) norms
• L p Norms of Certain Kernels on the N-Dimensional Torus
• NORMS OF DIRICHLET KERNELS AND SOME OTHER TRIGONOMETRIC POLYNOMIALS IN $ L_p$-SPACES
• Notes on the Theory of Series (XIII): Some New Properties of Fourier Constants
• On the coefficients of multiple Fourier series in $ L_p$-spaces
• On Double Cosine, Sine, and Walsh Series with Monotone Coefficients

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