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 $\mathbb C$ 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 $\mathcal D_m^2(\mathbb D_R,\mu^R_{\alpha,\beta})$ and then we study its asymptotic behavior when the parameter $\alpha$ goes to infinity and to $(-1)$ 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