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

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.