Functiones et Approximatio Commentarii Mathematici

Estimates of the approximation error for abstract sampling type operators in Orlicz spaces

Carlo Bordaro and Ilaria Mantellini

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Abstract

We get some inequalities concerning the modular distance $I^\varphi_G[Tf -f]$ for bounded functions $f:G\rightarrow \mathbb{R}.$ Here $G$ is a locally compact Hausdorff topological space provided with a regular and $\sigma$-finite measure $\mu_G,$ $I^\varphi_G$ is the modular functional generating the Orlicz spaces $L^\varphi(G)$ and $T$ is a nonlinear integral operator of the form $$(Tf)(s) = \int_H K(s,t, f(t)) d\mu_H(t),$$ where $H$ is a closed subset of $G$ endowed with another regular and $\sigma$-finite measure $\mu_H.$ As a consequence we obtain a convergence theorem for a net of such operators. Some applications to discrete operators are given.

Article information

Source
Funct. Approx. Comment. Math., Volume 36 (2006), 45-70.

Dates
First available in Project Euclid: 18 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.facm/1229616441

Digital Object Identifier
doi:10.7169/facm/1229616441

Mathematical Reviews number (MathSciNet)
MR2296638

Subjects
Primary: 47G10: Integral operators [See also 45P05]
Secondary: 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05] 26D15: Inequalities for sums, series and integrals 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
Sampling operators discrete operators Orlicz spaces moduli of continuity

Citation

Bordaro, Carlo; Mantellini, Ilaria. Estimates of the approximation error for abstract sampling type operators in Orlicz spaces. Funct. Approx. Comment. Math. 36 (2006), 45--70. doi:10.7169/facm/1229616441. https://projecteuclid.org/euclid.facm/1229616441


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