Aïssaoui, N. Maximal operators, Lebesgue points and quasicontinuity in strongly nonlinear potential theory. (English) Zbl 1052.46019 Acta Math. Univ. Comen., New Ser. 71, No. 1, 35-50 (2002). 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. Cited in 2 Documents 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 Keywords:Orlicz spaces; capacities; Bessel potential; maximal operators; Lebesgue point; quasicontinuity PDFBibTeX XMLCite \textit{N. Aïssaoui}, Acta Math. Univ. Comen., New Ser. 71, No. 1, 35--50 (2002; Zbl 1052.46019) Full Text: EuDML EMIS