Nikol'skii's inequality for different metrics and properties of the sequence of norms of the Fourier sums of a function in the Lorentz space

DOI10.1134/S0081543806040158zbMath1351.42012OpenAlexW2000449352MaRDI QIDQ2342267

Yanyan Li

Publication date: 11 May 2015

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543806040158

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Interpolation between normed linear spaces (46B70) Fourier series and coefficients in several variables (42B05) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (9)

Estimates for the Kolmogorov widths of the Nikol'skii-Besov-Amanov classes in the Lorentz space ⋮ ON THE INEQUALITY OF DIFFERENT METRICS FOR MULTIPLE FOURIER-HAAR SERIES ⋮ Some New Fourier and Jackson-Nikol'skii Type Inequalities In Unbounded Orthonormal Systems ⋮ EESTIMATES OF BEST APPROXIMATIONS OF FUNCTIONS WITH LOGARITHMIC SMOOTHNESS IN THE LORENTZ SPACE WITH ANISOTROPIC NORM ⋮ Net spaces and boundedness of integral operators ⋮ A Lizorkin Theorem on Fourier Series Multipliers for Strong Regular Systems ⋮ On approximation orders of functions of several variables in the Lorentz space ⋮ On multipliers of Fourier series in the Haar system ⋮ Multipliers of double Fourier-Haar series

Cites Work

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• Nikol'skij inequalities for trigonometric polynomials in Lorentz spaces
• Interpolation theorems for anisotropic function spaces and their applications
• Multivariate Rearrangements and Banach Function Spaces with Mixed Norms
• Probabilities in Proofreading
• Net spaces and inequalities of Hardy-Littlewood type
• Fonctions continues et fonctions bornées non adhérentes dans $L^{∞}(T)$ à la suite de leurs sommes partielles de Fourier

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