The Bergman kernel functions of certain unbounded domains

A study of the Bergman projection in certain Hartogs domains

We show that the Bergman projection does not preserve smoothness of functions in some pseudoconvex domains in the space of two complex variables.

Zeroes of the Bergman kernel of Hartogs domains

We exhibit a class of bounded, strongly convex Hartogs domains with realanalytic boundary which are not Lu Qi-Keng, i.e. whose Bergman kernel function has a zero.

Szegö Kernels for Certain Unbounded Domains

Subharmonicity Properties of the Bergman Kernel and Some Other Functions Associated to Pseudoconvex Domains

Let D be a pseudoconvex domain in Ckt × C n z and let φ be a plurisubharmonic function in D. For each t we consider the ndimensional slice of D, Dt = {z; (t, z) ∈ D}, let φ be the restriction of φ to Dt and denote by Kt(z, ζ) the Bergman kernel of Dt with the weight function φ. Generalizing a recent result of Maitani and Yamaguchi (corresponding to n = 1 and φ = 0) we prove that logKt(z, z) is ...

The Bergman Kernel Function of Some Reinhardt Domains

The boundary behavior of the Bergman Kernel function of some Reinhardt domains is studied. Upper and lower bounds for the Bergman kernel function are found at the diagonal points (z, z̄). Let D be the Reinhardt domain D = { z ∈ C | ‖z‖α = n ∑