Explicit formulas for the Szegő kernel on certain weakly pseudoconvex domains

Abstract

The objective of this paper is to determine the Szegő kernel of the domain D = { ( z , ζ , w ) ∈ C n + m + 1 ; ℑ m w > ‖ z ‖ 2 + ‖ ζ ‖ 2 p } \mathcal {D} = \{ (z,\zeta ,w) \in {\mathbb {C}^{n + m + 1}};\Im {\text {m}}w > {\left \| z \right \|^2} + {\left \| \zeta \right \|^{2p}}\} explicitly in closed form.