Generalized smoothness and approximation of periodic functions in the spaces \(L_p\), \(1 < p < +\infty \)

DOI10.1134/S0001434619090104zbMath1439.42002OpenAlexW2981398323MaRDI QIDQ2291198

Konstantin V. Runovski

Publication date: 30 January 2020

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434619090104

zbMATH Keywords

modulus of smoothnessbest approximationgeneralized derivative

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Trigonometric approximation (42A10) Best approximation, Chebyshev systems (41A50) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17)

Related Items (3)

Direct theorems on approximation of periodic functions with high generalized smoothness ⋮ Multiplicator type operators and approximation of periodic functions of one variable by trigonometric polynomials ⋮ Inverse theorems on the approximation of periodic functions with high generalized smoothness

Cites Work

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• Direct and converse theorems of the theory of approximation in the metric of \(L_p\) for \(0<p<1\)
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• Moduli of smoothness related to fractional Riesz-derivatives
• A direct theorem of approximation theory for a general modulus of smoothness
• Embedding theorems in constructive approximation
• Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes
• General Moduli of Smoothness and Approximation by Families of Linear Polynomial Operators
• Trigonometric polynomial approximation,K-functionals and generalized moduli of smoothness
• ON INTEGRAL INEQUALITIES FOR TRIGONOMETRIC POLYNOMIALS AND THEIR DERIVATIVES

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