Toeplitz operators and Carleson measures in strongly pseudoconvex domains

Details Toeplitz operators and Carleson measures in strongly pseudoconvex domains Toeplitz operators and Carleson measures in strongly pseudoconvex domains

2012-02-06

arxiv.org/abs/1202.1180v1

Mathematics

Complex Variables

36 pages

Scientific paper

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.

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