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Maximal operators, Lebesgue point and quasicontinuity in strongly nonlinear potential theory. (English) Zbl 1136.31314

Summary: Many maximal functions defined on some Orlicz spaces \(\mathbf L_A\) are bounded operators on \(\mathbf L_A\) 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 \(\mathbf L_A\) sense and we give an \((m,A)\)-quasicontinuous representative for \(f\) when \(\mathbf L_A\) is reflexive.

MSC:

31C45 Other generalizations (nonlinear potential theory, etc.)
47B38 Linear operators on function spaces (general)
42B25 Maximal functions, Littlewood-Paley theory