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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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