13 research outputs found
On the Lelong-Demailly numbers of plurisubharmonic currents
In this note we study the existence of the Lelong-Demailly number of a
negative plurisubharmonic current with respect to a positive plurisubharmonic
function on an open subset of \C^n. Then we establish some estimates of the
Lelong-Demailly numbers of positive or negative plurisubharmonic currents
Meromorphic Bergman spaces
In this paper we introduce new spaces of holomorphic functions on the pointed
unit disc of that generalize classical Bergman spaces. We prove
some fundamental properties of these spaces and their dual spaces. We finish
the paper by extending Hardy-Littlewood and Fej\'er-Riesz inequalities to these
spaces with an application on Toeplitz operators.Comment: 15 pages, no figur
Asymptotic results on modified Bergman-Dirichlet spaces and examples of Segal-Bargmann transforms
In this paper, we start by introducing the modified Bergman-Dirichlet space
and then we study its
asymptotic behavior when the parameter goes to infinity and to
to obtain respectively the modified Bargmann-Dirichlet and the modified
Hardy-Dirichlet spaces with their reproducing kernels. Finally, we give some
examples of Segal-Bargmann transforms of those spaces.Comment: 19 page