arXiv subjects

H. Bommier-Hato

Publications and source records attributed to H. Bommier-Hato.

2 recordsLinked to original sources

arXiv2020

Small Hankel operators on vector valued generalzed Fock spaces

We study small Hankel operators $h_b$ with operator-valued holomorphic symbol $b$ on a class of vector-valued Fock type spaces. We show that the boundedness / compactness of $h_b$ is equivalent to the membership of $b$ to a specific growth space, which is described via a Littlewood-Paley type condition and a Bergman type projection, and estimate the norm of $h_b$. We also establish some properties of duality and density for these Fock spaces.

math.FA↗

arXiv2020

Volterra operators and Hankel forms on Bergman spaces of Dirichlet series

For a Dirichlet series g, we study the Volterra operator Tg of symbol g, acting on a class of weighted Hilbert spaces of Dirichlet series. We obtain sufficient / necessary conditions for Tg to be bounded (resp. compact), involving BMO and Bloch type spaces on some half-plane. We also investigate the membership of Tg in Schatten classes. We also relate the boundedness of Tg to the boundedness of a multiplicative Hankel form of symbol g.

math.FA↗