Toeplitz operators and Carleson measures in strongly pseudoconvex domains

Marco Abate (1) , Jasmin Raissy (2) , Alberto Saracco (3)

1 Dipartimento di Matematica [Pisa]
2 Dipartimento di Matematica e Applicazioni [Milano]
3 Department of Mathematics and Computer Science [Parma]

We study mapping properties of Toeplitz operators associated to a finite positive Borel measure on a bounded strongly pseudoconvex domain $D$ in $n$ complex variables. In particular, we give sharp conditions on the measure ensuring that the associated Toeplitz operator maps the Bergman space $A^p(D)$ into $A^r(D)$ with $r>p$, generalizing and making more precise results by Cuckovic and McNeal. To do so, we give a geometric characterization of Carleson measures and of vanishing Carleson measures of weighted Bergman spaces in terms of the intrinsic Kobayashi geometry of the domain, generalizing to this setting results obtained by Kaptanoglu for the unit ball.

Domaines: Variables complexes [math.CV]; Systèmes dynamiques [math.DS]

Marco Abate, Jasmin Raissy, Alberto Saracco. Toeplitz operators and Carleson measures in strongly pseudoconvex domains. Journal of Functional Analysis, 2012, 263 (11), pp.3449-3491. ⟨hal-00968275⟩