On the continuity of Bessel potentials in Orlicz spaces. (English) Zbl 0852.46028

It is shown that Bessel capacities in reflexive Orlicz spaces are non-increasing under orthogonal projection of sets. This is used to describe sets for which the potentials are continuous. In particular, for Bessel potentials, we have more information about their differentiability.
On the other hand we show that the null sets (for Bessel capacities in Orlicz spaces) are conserved by some special Lipschitzian maps.
The obtained results generalize those of N. G. Meyers and Yu. G. Reshetnyak, in the case of Lebesgue spaces.
Reviewer: N.Aïssaoui (Fès)


46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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