Geodesic
Approximation by nonlinear integral operators in some modular function spaces
Annales Polonici Mathematici, Tome 63 (1996) no. 2, pp. 173-182.

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Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function $f ∈ (L⁰(G))_{ϱ+η} ∩ Dom T$ is estimated, where $(Tf)(s) = ∫_G K(t-s,f(t))dt$ and K satisfies a generalized Lipschitz condition with respect to the second variable.
DOI : 10.4064/ap-63-2-173-182
Keywords: modular space, nonlinear integral operator, generalized Lipschitz condition, approximation by singular integrals

Carlo Bardaro 1 ; Julian Musielak 1 ; Gianluca Vinti 1

1 
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Carlo Bardaro; Julian Musielak; Gianluca Vinti. Approximation by nonlinear integral operators in some modular function spaces. Annales Polonici Mathematici, Tome 63 (1996) no. 2, pp. 173-182. doi : 10.4064/ap-63-2-173-182. http://geodesic.mathdoc.fr/articles/10.4064/ap-63-2-173-182/

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