Weighted tent spaces with Whitney averages: factorization, interpolation and duality. (English) Zbl 1335.42022
Summary: In this paper, we introduce a new scale of tent spaces, which covers the (weighted) tent spaces of Coifman-Meyer-Stein and of Hofmann-Mayboroda-McIntosh, and some other tent spaces considered by Dahlberg, Kenig-Pipher and Auscher-Axelsson in studying boundary value problems for elliptic systems. The strong factorizations within our tent spaces, with applications to quasi-Banach complex interpolation and to multiplier-duality theory, are then established. This way, we unify and extend the corresponding results obtained by Coifman-Meyer-Stein, Cohn-Verbitsky and Hytönen-Rosén.
MSC:
| 42B35 | Function spaces arising in harmonic analysis |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
Keywords:
tent spaces; Whitney averages; strong factorization; Calderón’s product; quasi-Banach complex interpolation; multipliers; duality theoryReferences:
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