SOME OPERATOR IDEAL PROPERTIES OF VOLTERRA OPERATORS ON BERGMAN AND BLOCH SPACES

Joelle Jreis (1) , Pascal Lefèvre (1)

1 LML - Laboratoire de Mathématiques de Lens

We characterize the integration operators V g with symbol g for which V g acts as an absolutely summing operator on weighted Bloch spaces B β and on weighted Bergman spaces A p α. We show that V g is r-summing on A p α , 1 ≤ p < ∞, if and only if g belongs to a suitable Besov space. We also show that there is no non trivial nuclear Volterra operators V g on Bloch spaces and on Bergman spaces.

Mots clés: r-summing operators; Nuclear operators; Volterra operators; Bergman spaces; Bloch spaces

Domaines: Analyse fonctionnelle [math.FA]

Joelle Jreis, Pascal Lefèvre. SOME OPERATOR IDEAL PROPERTIES OF VOLTERRA OPERATORS ON BERGMAN AND BLOCH SPACES. 2022. ⟨hal-03856765⟩