Subharmonicity Properties of the Bergman Kernel and Some Other Functions Associated to Pseudoconvex Domains
نویسنده
چکیده
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 a plurisubharmonic function in D. We also generalize an earlier results of Yamaguchi concerning the Robin function and discuss similar results in the setting of R.
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