Seminari di Sistemi Dinamici Olomorfi 2012-2013

seminar: Toeplitz operators and Carleson measures in strongly pseudoconvex domains

speaker: Marco Abate (Dipartimento di Matematica, Università di Pisa)

abstract: (Joint work with J. Raissy and A. Saracco)

We study mapping properties of Toeplitz operators associated to a finite positive Borel measure on a bounded strongly pseudoconvex domain. In particular, we give sharp conditions on the measure ensuring that the associated Toeplitz operator maps the Bergman space A^p 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.

timetable:
Tue 2 Apr, 14:30 - 15:30, Sala Conferenze Centro De Giorgi
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