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An extremality property of Szegő projections on Heisenberg groups
Gian Maria Dall'Ara, Bernhard Lamel
We prove that Heisenberg groups, a.k.a. the boundaries of Siegel domains, minimize the operator norm of the Szegő projection in a large class of weighted CR manifolds of hype…
The core of the Levi distribution
Gian Maria Dall'Ara, Samuele Mongodi
We introduce a new geometrical invariant of CR manifolds of hypersurface type, which we dub the "Levi core" of the manifold. When the manifold is the boundary of a smooth bounded p…
Around (un)boundedness of Bergman and Szegö projections
Gian Maria Dall'Ara
We consider the problem of (un)boundedness for a wide class of orthogonal projections, including Bergman projections on domains in complex manifolds and Szegö projections on…
On noncompactness of the -Neumann problem on pseudoconvex domains in
Gian Maria Dall'Ara
In this paper we deal with the following question: is it true that any bounded smooth pseudoconvex domain in whose boundary contains a -dimensional complex manifo…
Coercivity of weighted Kohn Laplacians: the case of model monomial weights in
Gian Maria Dall'Ara
The weighted Kohn Laplacian is a natural second order elliptic operator associated to a weight and acting on -forms, which pla…
Pointwise estimates of weighted Bergman kernels in several complex variables
Gian Maria Dall'Ara
We prove new pointwise bounds for weighted Bergman kernels in , whenever a coercivity condition is satisfied by the associated weighted Kohn Laplacian on -form…