We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in L2(e−2φ) where φ is a subharmonic function with ∆φ a doubling measure. We derive estimates for the canonical solution operator to the inhomogeneous CauchyRiemann equation and we characterize the compactness of this operator in terms of ∆φ.

The aim of this work is to find optimal estimates for the Bergman kernels classical domains ℜ

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending [15]. We compute the second coefficient b1 in the asymptotic expansion using the method of [24].

In this paper, we investigate singular integral operators induced by the Bergman kernel and Szegö on irreducible bounded symmetric domain in its standard Harish-Chandra realization. We completely characterize when Bergman-type Szegö-type belong to Schatten class operator ideals several analytic numerical invariants of domain. These results not only generalize a recent result Hilbert unit ball d...