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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.)