Some \(s\)-numbers of an integral operator of Hardy type on \(L^{p(\cdot)}\) spaces

DOI10.1016/j.jfa.2009.02.015zbMath1175.47017OpenAlexW2105409896MaRDI QIDQ1028340

David E. Edmunds, Aleš Nekvinda, Jan Lang

Publication date: 30 June 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2009.02.015

zbMATH Keywords

compactnessHardy-type operator\(s\)-numbersvariable exponent function spaces

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) Riesz operators; eigenvalue distributions; approximation numbers, (s)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators (47B06) Integral operators (47G10)

Related Items

Some \(s\)-numbers of an integral operator of Hardy type in Banach function spaces ⋮ Stability of the norm-eigenfunctions of the \(p(\cdot)\)-Laplacian ⋮ Embeddings, Hardy operators and nonlinear problems ⋮ Convergence properties of modular eigenfunctions for the \(p(\cdot)\)-Laplacian ⋮ \(\Gamma\)-convergence of the energy functionals for the variable exponent \(p(\cdot)\)-Laplacian and stability of the minimizers with respect to integrability ⋮ Gelfand numbers of embeddings of Schatten classes ⋮ Boundedness of solutions of the non-uniformly convex, non-standard growth Laplacian ⋮ Extension of a result by Lindquist to Lebesgue spaces with variable exponents ⋮ Estimates of \(s\)-numbers of a Sobolev embedding involving spaces of variable exponent

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bernstein widths of Hardy-type operators in a non-homogeneous case
• Behaviour of the approximation numbers of a Sobolev embedding in the one-dimensional case.
• Improved estimates for the approximation numbers of Hardy-type operators.
• Estimates for \(n\)-widths of the Hardy-type operators. Addendum to: ``Improved estimates for the approximation numbers of the Hardy-type operators [J.~Approximation Theory 121, No.\,1, 61--70 (2003; Zbl 1035.47009)]
• Über die Ungleichung, welche die Integrale über eine Potenz einer Funktion und über eine andere Potenz ihrer Ableitung verbindet
• SPECTRAL THEORY AND EMBEDDINGS OF SOBOLEV SPACES
• Bad properties of the Bernstein numbers
• Approximation numbers and Kolmogorov widths of Hardy‐type operators in a non‐homogeneous case