Holomorphic Jackson's theorems in polydiscs

DOI10.1016/J.JAT.2005.02.005zbMath1070.41007OpenAlexW2090669495MaRDI QIDQ557554

Mingzhi Wang, Guang Bin Ren

Publication date: 30 June 2005

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

Full work available at URL: https://doi.org/10.1016/j.jat.2005.02.005

zbMATH Keywords

Sobolev spaceHardy spaceLipschitz spaceBergman spacepolynomial approximationpolydiscmodulus of continuitymodulus of smoothnessJackson-type inequalitypolydisc algebraBergman-type spacegeneralized Jackson's kernelJackson's theorem

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Multidimensional problems (41A63) (H^p)-spaces, Nevanlinna spaces of functions in several complex variables (32A35) Bergman spaces of functions in several complex variables (32A36) Algebras of holomorphic functions of several complex variables (32A38)

Related Items (7)

Jackson's theorem on bounded symmetric domains ⋮ Multidimensional intertwining Leja sequences and applications in bidimensional Lagrange interpolation ⋮ Density of polyanalytic polynomials in complex and quaternionic polyanalytic weighted Bergman spaces ⋮ Polynomial approximation in Bergman spaces ⋮ Quantitative approximations by convolution polynomials in Bergman spaces ⋮ Jackson's theorem in \(Q_{p}\) spaces ⋮ Gradient estimates and Jackson's theorem in \(Q_\mu \) spaces related to measures

Cites Work

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• \(q\)-moduli of continuity in \(H^{p}(\mathbb D)\), \(p>0\) and an inequality of Hardy and Littlewood
• On theorems of Jackson and Bernstein type in the complex plane
• Jackson theorems in Hardy spaces and approximation by Riesz means
• Harmonic version of Jackson's theorem in the complex plane
• On the best polynomial approximation in some Banach spaces for functions analytical in the unit disk
• APPROXIMATION OF FUNCTIONS OF CLASSH^p, 0 <p≤ 1
• THEOREMS OF JACKSON TYPE IN $ H^p$, $ 0 < p < 1$
• Extensions of D. Jackson's Theorem on Best Complex Polynomial Mean Approximation
• Degree of Approximation by Polynomials in the Complex Domain. (AM-9)

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