Extension of the operator of best polynomial approximation in \(L^p(\Omega )\)

DOI10.1016/j.jmaa.2010.10.037zbMath1208.41021OpenAlexW2076871124MaRDI QIDQ624615

Héctor H. Cuenya

Publication date: 9 February 2011

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.10.037

zbMATH Keywords

best approximation\(L^p\)-normgeneralized polynomial

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Approximation by arbitrary linear expressions (41A45)

Related Items (10)

Existence and characterization of best \(\varphi\)-approximations by linear subspaces ⋮ Extended Best Polynomial Approximation Operator in Orlicz Spaces ⋮ Taylor's inequalities in Orlicz–Sobolev type spaces ⋮ On a generalization of the extended best polynomial approximation operator in Orlicz–Lorentz spaces ⋮ Extended best polynomial approximation operator in Orlicz–Lorentz spaces ⋮ Multivalued Extended BestΦ-Polynomial Approximation Operator ⋮ Inequalities in \(L^{p-1}\) for the extended \(L^p\) best approximation operator ⋮ Inequalities for the extended best polynomial approximation operator in Orlicz spaces ⋮ Extension of the Best Constant Approximation Operator in Orlicz Spaces ⋮ Extended best \(L^p\)-approximation is near-best approximation in \(L^q, p - 1 \leq q < p\)

Cites Work

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• Extension of the best approximation operator in Orlicz spaces
• Isotonic approximation in \(L_ s\).
• Extension of the best approximation operator in Orlicz spaces and weak-type inequalities
• A Lebesgue type differentiation theorem for best approximations by constants in Orlicz spaces
• Isotonic approximation in \(L_{1}\)
• Weak inequalities for maximal functions in Orlicz-Lorentz spaces and applications
• On Smoothest Interpolants
• Maximal inequalities and Lebesgue's differentiation theorem for best approximant by constant over balls

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