ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXI, 1(2002)
p. 35

Maximal operators, Lebesgue points and quasicontinuity in strongly nonlinear potential theory
N. Aissaoui

Abstract.  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 $L_A$ is reflexive.

AMS subject classification:  46E35 31B15
Keywords:  Orlicz spaces, capacities, Bessel potential, maximal operators, Lebesgue point, quasicontinuity.