## Maximal operators, Lebesgue points and quasicontinuity in strongly nonlinear potential theory.(English)Zbl 1052.46019

Summary: Many maximal functions defined on some Orlicz spaces $$L_A$$ are bounded operators on $$L_A$$ if and only if they satisfy a capacitary weak inequality. We show also that $$(m,A)$$-quasievery $$x$$ is a Lebesgue point for $$f$$ in $$L_A$$ sense and we give an $$(m,A)$$-quasicontinuous representative for $$f$$ when $$L_A$$ is reflexive.

### MSC:

 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B25 Maximal functions, Littlewood-Paley theory
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