# Approximation by nonlinear integral operators in some modular function spaces

Carlo Bardaro; Julian Musielak; Gianluca Vinti

Annales Polonici Mathematici (1996)

- Volume: 63, Issue: 2, page 173-182
- ISSN: 0066-2216

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topCarlo Bardaro, Julian Musielak, and Gianluca Vinti. "Approximation by nonlinear integral operators in some modular function spaces." Annales Polonici Mathematici 63.2 (1996): 173-182. <http://eudml.org/doc/262585>.

@article{CarloBardaro1996,

abstract = {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.},

author = {Carlo Bardaro, Julian Musielak, Gianluca Vinti},

journal = {Annales Polonici Mathematici},

keywords = {modular space; nonlinear integral operator; generalized Lipschitz condition; approximation by singular integrals; locally compact Hausdorff group; Haar measure},

language = {eng},

number = {2},

pages = {173-182},

title = {Approximation by nonlinear integral operators in some modular function spaces},

url = {http://eudml.org/doc/262585},

volume = {63},

year = {1996},

}

TY - JOUR

AU - Carlo Bardaro

AU - Julian Musielak

AU - Gianluca Vinti

TI - Approximation by nonlinear integral operators in some modular function spaces

JO - Annales Polonici Mathematici

PY - 1996

VL - 63

IS - 2

SP - 173

EP - 182

AB - 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.

LA - eng

KW - modular space; nonlinear integral operator; generalized Lipschitz condition; approximation by singular integrals; locally compact Hausdorff group; Haar measure

UR - http://eudml.org/doc/262585

ER -

## References

top- [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. Zbl0804.46034
- [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. Zbl0832.46020
- [3] C. Bardaro and G. Vinti, Modular approximation by nonlinear integral operators on locally compact groups, Comment. Math. Prace Mat., to appear. Zbl0972.47034
- [4] J. Musielak, Nonlinear approximation in some modular function spaces. I, Math. Japon. 38 (1993), 83-90. Zbl0779.46017
- [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. Zbl0823.41018
- [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.

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