Properties of moduli of smoothness in \(L_p (\mathbb{R}^d)\)

DOI10.1016/j.jat.2020.105423zbMath1450.41004arXiv1907.12788OpenAlexW3019752015MaRDI QIDQ783712

Yurii S. Kolomoitsev, Sergey Yu. Tikhonov

Publication date: 4 August 2020

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.12788

zbMATH Keywords

\(K\)-functionalentire functions of exponential typemoduli of smoothnessJackson inequalitiesMarchaud inequalitiesrealization of the \(K\)-functionalUlyanov inequalities

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Fractional derivatives and integrals (26A33) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) Inequalities for sums, series and integrals (26D15) Rate of convergence, degree of approximation (41A25)

Related Items (14)

Uniform approximation by multivariate quasi-projection operators ⋮ Approximation properties of the sampling Kantorovich operators: regularization, saturation, inverse results and Favard classes in \(L^p\)-spaces ⋮ A note on \(K\)-functional, modulus of smoothness, Jackson theorem and Bernstein-Nikolskii-Stechkin inequality on Damek-Ricci spaces ⋮ A characterization of the rate of the simultaneous approximation by generalized sampling operators and their Kantorovich modification ⋮ On generalized \(K\)-functionals in \(L_p\) for \(0<p<1\) ⋮ Bourgain-Brezis-Mironescu-Maz'ya-Shaposhnikova limit formulae for fractional Sobolev spaces via interpolation and extrapolation ⋮ Sharp \(L_p\)-error estimates for sampling operators ⋮ Sharp approximation theorems and Fourier inequalities in the Dunkl setting ⋮ Fourier transforms and fractional Lipschitz and Nikol'skii classes in uniform metric ⋮ Embeddings and characterizations of Lipschitz spaces ⋮ On various moduli of smoothness and \(K\)-functionals ⋮ Approximation by multivariate quasi-projection operators and Fourier multipliers ⋮ Smoothness of functions versus smoothness of approximation processes ⋮ Besov spaces with generalized smoothness and summability of multiple Fourier series

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