BERGMAN AND HARDY SPACES ON MODEL DOMAINS

摘要

Weakly pseudoconvex domains of this kind were investigated by McNeal [McN1] and Nagel, Rosay, Stein and Wainger [NRSW1], [NRSW2]. For the case where p(z) = |z|~k, k ∈ N, Greiner and Stein [GS] found an explicit expression for the Szegoe kernel of Ω_p. If p is a subharmonic function, which depends only on the real or only on the imaginary part of z, then one can find analogous expressions and estimates in [N] (see also [Has1]). In [D] and in [K] properties of the Szegoe projection for such domains are studied. The asymptotic behavior of the corresponding Szegoe kernel was investigated in [Han] and [Has2]. There have been several recent papers obtaining explicit formulas for the Bergman kernel function on various weakly pseudoconvex domains ([D'A], [BFS], [FH2] and [FH3]).