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Instability of capacity in Orlicz spaces. (English) Zbl 0896.46020
Summary: We describe the instability of certain capacities in the Orlicz spaces. Our results generalize some of those obtained by C. Fernström in [Ark. Mat. 15, 241-252 (1977; Zbl 0372.31003)] and Theorem 9 of L. I. Hedberg in [Math. Z. 129, 299-319 (1972; Zbl 0243.31014)] in the case of Lebesgue spaces.

MSC:
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
31B15 Potentials and capacities, extremal length and related notions in higher dimensions
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