Absolutely summing Carleson embeddings on Hardy spaces

Pascal Lefèvre (1) , Luis Rodríguez-Piazza (2)

1 LML - Laboratoire de Mathématiques de Lens
2 Departamento de Analisis Matematico

We consider the Carleson embeddings of the classical Hardy spaces (on the disk) into a L p (µ) space, where µ is a Carleson measure on the unit disk. This includes the case of composition operators. We characterize such operators which are r-summing on H p , where p > 1 and r ≥ 1. This completely extends the former results on the subject and solves a problem open since the early seventies.

Domaines: Analyse fonctionnelle [math.FA]

Pascal Lefèvre, Luis Rodríguez-Piazza. Absolutely summing Carleson embeddings on Hardy spaces. 2017. ⟨hal-01376926v2⟩