  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.
