A simple characterization of weighted Sobolev spaces with bounded multiplication operator

DOI10.1016/j.jat.2008.01.003zbMath1221.41007OpenAlexW2023774095MaRDI QIDQ935081

José M. Rodríguez

Publication date: 31 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.jat.2008.01.003

zbMATH Keywords

weighted Sobolev spacesSobolev orthogonal polynomialsmultiplication operatorlocation of zeros

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Vector-valued measures and integration (46G10) Approximation by polynomials (41A10)

Related Items

Zeros of Sobolev orthogonal polynomials via Muckenhoupt inequality with three measures ⋮ Weighted Sobolev spaces: Markov-type inequalities and duality ⋮ Zero location and asymptotic behavior for extremal polynomials with non-diagonal Sobolev norms ⋮ Concerning asymptotic behavior for extremal polynomials associated to nondiagonal Sobolev norms ⋮ Measurable diagonalization of positive definite matrices ⋮ Muckenhoupt inequality with three measures and applications to Sobolev orthogonal polynomials ⋮ The multiplication operator, zero location and asymptotic for non-diagonal Sobolev norms ⋮ Sobolev spaces with respect to measures in curves and zeros of Sobolev orthogonal polynomials

Cites Work

• Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials. I
• On polynomials orthogonal with respect to certain Sobolev inner products
• Weighted Weierstrass' theorem with first derivatives
• Zero location and \(n\)th root asymptotics of Sobolev orthogonal polynomials
• Orthogonal polynomials and approximation in Sobolev spaces
• Boundedness properties for Sobolev inner products
• Weierstrass' theorem with weights
• Approximation by polynomials and smooth functions in Sobolev spaces with respect to measures
• Weighted Sobolev spaces on curves
• Weierstrass's theorem in weighted Sobolev spaces with \(k\) derivatives
• A Kolmogorov-Szego-Krein type condition for weighted Sobolev spaces
• Weighted Norm Inequalities for the Hardy Maximal Function
• Sobolev orthogonal polynomials in the complex plane
• Weierstrass' theorem in weighted Sobolev spaces
• The multiplication operator in Sobolev spaces with respect to measures
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