Some new Fourier inequalities for unbounded orthogonal systems in Lorentz-Zygmund spaces

DOI10.1186/s13660-020-02344-6zbMath1503.26039OpenAlexW3015936694MaRDI QIDQ2069358

Dag Lukkassen, Lars-Erik Persson, G. A. Akishev

Publication date: 20 January 2022

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

Full work available at URL: https://doi.org/10.1186/s13660-020-02344-6

zbMATH Keywords

inequalitiesFourier seriesFourier coefficientsLorentz-Zygmund spacesunbounded orthogonal systems

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) Inequalities for sums, series and integrals (26D15) Fourier series and coefficients in several variables (42B05) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Inequalities for trigonometric functions and polynomials (26D05) Other analytical inequalities (26D20) Zygmund spaces (30H40)

Related Items (1)

Some New Fourier and Jackson-Nikol'skii Type Inequalities In Unbounded Orthonormal Systems

Cites Work

• Embedding Nikol'skiĭ classes into Lorentz spaces
• Some generalizations of the Hardy-Littlewood-Paley theorem
• Some Fourier inequalities for orthogonal systems in Lorentz-Zygmund spaces
• Quasi-monotone weight functions and their characteristics and applications
• Interpolation of Linear Operators
• Interpolation with a parameter function.
• Counterexamples for classical operators on Lorentz-Zygmund spaces
• Relations between summability of functions and their Fourier series
• On the coefficients of multiple Fourier series in $ L_p$-spaces
• On a Theorem of Pitt
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