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Orlicz-Hardy inequalities. (English) Zbl 1070.46018

Summary: We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of \(L^n\), this relationship is necessary and sufficient, thus extending results of Ancona, Lewis, and Wannebo.

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
26D15 Inequalities for sums, series and integrals
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