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We study mapping properties of Toeplitz operators associated to a finitepositive Borel measure on a bounded strongly pseudoconvex domain D in n complexvariables. In particular, we give sharp conditions on the measure ensuring thatthe associated Toeplitz operator maps the Bergman space A^p(D) into A^r(D) withr>p, generalizing and making more precise results by Cuckovic and McNeal. To doso, we give a geometric characterization of Carleson measures and of vanishingCarleson measures of weighted Bergman spaces in terms of the intrinsicKobayashi geometry of the domain, generalizing to this setting results obtainedby Kaptanoglu for the unit ball.

Toeplitz operators and Carleson measures in strongly pseudoconvex domains