Compactness of linear integral operators in ideal spaces of vector functions

DOI10.1216/JIE-2012-24-3-393zbMath1259.45009OpenAlexW2041885137WikidataQ57363350 ScholiaQ57363350MaRDI QIDQ1931289

Martin Väth

Publication date: 25 January 2013

Published in: Journal of Integral Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.jiea/1350925562

zbMATH Keywords

integral operatorBanach function spacemeasure of noncompactnessCarathéodory functionkernel operatorspaces of measurable functionsUrysohn operatorideal spacenon-measurable kernel

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) Other nonlinear integral equations (45G10) Integral operators (45P05) Integral operators (47G10) Abstract integral equations, integral equations in abstract spaces (45N05) Measures of noncompactness and condensing mappings, (K)-set contractions, etc. (47H08)

Cites Work

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• Compactness of integral operators in Banach function spaces
• On the Cauchy problem for ordinary differential equations in Banach spaces
• Measures of noncompactness and condensing operators. Transl. from the Russian by A. Iacob
• Compactness estimates for integral operators of vector functions with nonmeasurable kernels
• Convergence theorems and measures of noncompactness for noncompact Urysohn operators in ideal spaces
• On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions
• Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces
• The existence of non-trivial bounded functionals implies the Hahn-Banach extension theorem

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