2026/08/01 by Amiran Gogatishvili, Ron Kerman, Susanna Spektor
Mathematics · #math.AP #math.CA #math.FA #msc:42B25 #msc:46E30 #msc:46B40
16 pages
arxiv created 2026/08/01 · arxiv updated 2026/08/04
We prove that the largest Orlicz space into which the Hardy averaging operator maps coincides with the largest rearrangement-invariant (r.i.) space mapping into that space; in other words, the optimal Orlicz domain is automatically the optimal r.i. domain. More generally, we show that every Luxemburg--Orlicz norm is equivalent to a sublinear functional which makes more computable a certain expression for a dual norm arising in the \K-theory of interpolation. As applications we obtain Orlicz-space mapping properties for the Hardy--Littlewood maximal function, approximate identities and Calderón--Zygmund singular integral operators. These mapping properties are shown to be optimal for the Hardy-Littlewood maximal function and the approximate identities.