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1996 | 63 | 2 | 173-182
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Approximation by nonlinear integral operators in some modular function spaces

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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.
Twórcy
  • Dipartimento di Matematica, Università degli Studi, via Vanvitelli, 1, 06123 Perugia, Italy
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
  • Dipartimento di Matematica, Università degli Studi, via Vanvitelli, 1, 06123 Perugia, Italy
Bibliografia
  • [1] C. Bardaro, J. Musielak and G. Vinti, Modular estimates and modular convergence for a class of nonlinear operators, Math. Japon. 39 (1994), 7-14.
  • [2] C. Bardaro, J. Musielak and G. Vinti, On absolute continuity of a modular connected with strong summability, Comment. Math. Prace Mat. 34 (1994), 21-33.
  • [3] C. Bardaro and G. Vinti, Modular approximation by nonlinear integral operators on locally compact groups, Comment. Math. Prace Mat., to appear.
  • [4] J. Musielak, Nonlinear approximation in some modular function spaces. I, Math. Japon. 38 (1993), 83-90.
  • [5] J. Musielak, On the approximation by nonlinear integral operators with generalized Lipschitz kernel over a locally compact abelian group, Comment. Math. Prace Mat. 34 (1995), 153-164.
  • [6] J. Musielak, On some linearly indexed families of submeasures, to appear in Atti del Convegno 'Real Analysis and Measure Theory' (Ischia July 1-6, 1994) and in Atti Sem. Mat. Fis. Univ. Modena.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-apmv63z2p173bwm
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