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Nonlinear approximation in some modular function spaces. I. (English) Zbl 0779.46017
The aim in this paper is to relate properties of a locally compact group \(G\) to those of a modular \(\rho\) on a function space \(F\) on \(G\). The discussion concerns the \(\rho\)-modulus of continuity of functions in \(F\) and certain filters of (nonlinear) integral operators approximating the identity on \(F\).

MSC:
46A80 Modular spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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