Kolmogorov widths and approximation numbers of Sobolev classes with singular weights

DOI10.1090/S1061-0022-2012-01229-XzbMath1275.41033OpenAlexW2017694282MaRDI QIDQ2849045

A. A. Vasil'eva

Publication date: 16 September 2013

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-2012-01229-x

zbMATH Keywords

approximation numbersKolmogorov widthsweighted Sobolev classes

Mathematics Subject Classification ID

Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (4)

Widths of weighted Sobolev classes with constraints \(f(a) = \cdots = f^{(k-1)}(a) = f^{(k)}(b) = \cdots = f^{(r-1)}(b) = 0\) and the spectra of nonlinear differential equations ⋮ Embedding theorems for a weighted Sobolev class in the space \(L_{q,v}\) with weights having a singularity at a point: case \(v\not\in L_{q}^{1}\) ⋮ Estimate for the entropy numbers of the weighted Hardy operators that act from Banach space to \(q\)-Banach space ⋮ Unnamed Item

Cites Work

• Entropy numbers of embeddings of function spaces with Muckenhoupt weights. III: Some limiting cases
• Weighted inequalities of Hardy type
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• Entropy and approximation numbers of embeddings of function spaces with Muckenhoupt weights. I
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• Criterion for the existence of a continuous embedding of a weighted Sobolev class on a closed interval and on a semiaxis
• Estimates for the widths of weighted Sobolev classes
• Asymptotic estimates for the approximation and entropy numbers of a one-weight Riemann-Liouville operator
• DIAMETERS OF SETS IN FUNCTION SPACES AND THE THEORY OF BEST APPROXIMATIONS
• s-Numbers of operators in Banach spaces
• DIAMETERS OF SETS IN NORMED LINEAR SPACES AND THE APPROXIMATION OF FUNCTIONS BY TRIGONOMETRIC POLYNOMIALS
• Weighted Norm Inequalities of Hardy Type for a Class of Integral Operators
• Approximation and entropy numbers of Volterra operators with application to Brownian motion
• Approximation numbers and Kolmogorov widths of Hardy‐type operators in a non‐homogeneous case
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