Weighted tent spaces with Whitney averages: factorization, interpolation and duality

Yi Huang (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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 elliptic equations. The strong factorizations within our tent spaces, with applications to quasi-Banach complex interpolation and to multiplier-duality theory, are established. This way, we unify and extend the corresponding results obtained by Coifman-Meyer-Stein, Cohn-Verbitsky and Hytönen-Rosén.

Mots clés: strong factorization; Calderón's product; multipliers and duality theory; Tent spaces; Whitney averages; multipliers and duality theory.; quasi-Banach complex interpolation

Domaines: Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Yi Huang. Weighted tent spaces with Whitney averages: factorization, interpolation and duality. Mathematische Zeitschrift, 2016, 282 (3-4), pp.913-933. ⟨10.1007/s00209-015-1570-0⟩. ⟨hal-00803611v2⟩