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Strong and weak type inequalities for some classical operators in Orlicz spaces. (English) Zbl 0940.46015

A characterization is given of the pairs of Young functions \(A\) and \(B\) having the property that some classical operators of harmonic analysis, such as (fractional) maximal functions, Riesz potentials and certain singular integrals, are of strong or weak type from the Orlicz space \(L^A\) into \(L^B\). Bounds for Orlicz norms of solutions to elliptic boundary value problems are also derived.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25 Maximal functions, Littlewood-Paley theory
35B45 A priori estimates in context of PDEs
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