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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