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Alberto Saracco

Publications and source records attributed to Alberto Saracco.

27 records · Page 2Linked to original sources
arXiv2012

Toeplitz operators and Carleson measures in strongly pseudoconvex domains

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.

math.CV↗
arXiv2009

Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains

We characterize using the Bergman kernel Carleson measures of Bergman spaces in strongly pseudoconvex bounded domains in several complex variables, generalizing to this setting theorems proved by Duren and Weir for the unit ball. We also show that uniformly discrete (with respect to the Kobayashi distance) sequences give examples of Carleson measures, and we compute the speed of escape to the boundary of uniformly discrete sequences in strongly pseudoconvex domains, generalizing results obtained in the unit ball by Jevtić, Massaneda and Thomas, by Duren and Weir, and by MacCluer.

math.CV↗
arXiv2008

Cohomology and removable subsets

Let X be a (connected and reduced) complex space. A q-collar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions) hypersurfaces. Finiteness and vanishing cohomology theorems obtained in math/0503490 and math/0701549 for semi q-coronae are generalized in this context and lead to results on extension problem and removable sets for sections of coherent sheaves and analytic subsets.

math.CV↗
arXiv2007

Hyperbolicity in unbounded convex domains

We provide several equivalent characterizations of Kobayashi hyperbolicity in unbounded convex domains in terms of peak and anti-peak functions at infinity, affine lines, Bergman metric and iteration theory.

math.CV↗
arXiv2007

Semi-global extension of maximally complex submanifolds

Let A be a domain of the boundary of a strictly pseudoconvex domain Ωof C^n and M a smooth, closed, maximally complex submanifold of A. We find a subdomain \widetilde A of Ω, depending only on Ωand A, and a complex subvariety W of \widetilde A such that bW\cap A = M. Moreover, a generalization to analytic sets of depth at least 4 is given.

math.CV↗
arXiv2006

Non compact boundaries of complex analytic varieties

We treat the boundary problem for complex varieties (with isolated singularities) of dimension greater than one, which are contained in a suitable class of strictly pseudoconvex, unbounded domains of C^n.

math.CV↗
arXiv2005

Cohomology and extension problems for semi q-coronae

We prove some extension theorems for analytic objects, in particular sections of a coherent sheaf, defined in semi q-coronae of a complex space. Semi q-coronae are domains whose boundary is the union of a Levi flat part, a q-pseudoconvex part and a q-pseudoconcave part. Such results are obtained mainly using cohomological techniques.

math.CV↗