On moduli of smoothness and \(K\)-functionals of fractional order in the Hardy spaces

DOI10.1007/S10958-012-0677-7zbMath1268.41012OpenAlexW2001779765MaRDI QIDQ1762514

Yurii S. Kolomoitsev

Publication date: 27 November 2012

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-012-0677-7

zbMATH Keywords

Hardy spacesmoduli of smoothnessfractional derivativeK-functional

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Rate of convergence, degree of approximation (41A25) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Approximation by arbitrary linear expressions (41A45)

Related Items (2)

On generalized \(K\)-functionals in \(L_p\) for \(0<p<1\) ⋮ Realization and characterization of modulus of smoothness in weighted Lebesgue spaces

Cites Work

• On the representation of a function as an absolutely convergent Fourier integral
• \(q\)-moduli of continuity in \(H^{p}(\mathbb D)\), \(p>0\) and an inequality of Hardy and Littlewood
• On some approximation properties of real Hardy spaces \((0<p\leq 1)\)
• On the order of approximation of functions of \(H^ p({\mathbb{R}})\) \((0<p\leq 1)\) by certain means of Fourier integrals
• Jackson theorems in Hardy spaces and approximation by Riesz means
• Approximation in the Frechet spaces \(L^p\;(0<p<1)\)
• Approximation properties in \(L_ p\), \(0<p<1\)
• Some properties of fractional integrals. II
• Moduli of smoothness and \(K\)-functionals in \(L_ p\), \(0<p<1\)
• Smooth functions
• Approximation of functions in $ H^p$, $ 0<p\le 1$, by generalized Riesz means with fractional exponents
• Some summability methods for power series of functions in $ H^p(D^n)$, $ 0<p<\infty$
• On the moduli of continuity ofH^pfunctions with 0<p<1
• Best Trigonometric Approximation, Fractional Order Derivatives and Lipschitz Classes
• Multipliers in the Hardy spaces $ H_p(D^m)$ with $ p\in (0,1 \rbrack $ and approximation properties of summability methods for power series
• A method of approximation in $ H^p$, $ 0<p\leqslant 1$
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