Approximation by nonlinear integral operators in some modular function spaces

Volume 63 / 1996

Carlo Bardaro, Julian Musielak, Gianluca Vinti Annales Polonici Mathematici 63 (1996), 173-182 DOI: 10.4064/ap-63-2-173-182


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.


  • Carlo Bardaro
  • Julian Musielak
  • Gianluca Vinti

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