, Volume 347, Issue 1, pp 1-13

On the growth of the Bergman kernel near an infinite-type point

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Abstract

We study diagonal estimates for the Bergman kernels of certain model domains in ${\mathbb{C}^{2}}$ near boundary points that are of infinite type. To do so, we need a mild structural condition on the defining functions of interest that facilitates optimal upper and lower bounds. This is a mild condition; unlike earlier studies of this sort, we are able to make estimates for non-convex pseudoconvex domains as well. This condition quantifies, in some sense, how flat a domain is at an infinite-type boundary point. In this scheme of quantification, the model domains considered below range—roughly speaking—from being “mildly infinite-type” to very flat at the infinite-type points.

This work is supported in part by a grant from the UGC under DSA-SAP, Phase IV.