Boundary behavior of the Bergman kernel function on strongly pseudoconvex domains with respect to weighted Lebesgue measure.

다국어 초록 (Multilingual Abstract)

The author proves pointwise estimates for the weighted Bergman kernel and its derivatives near the boundary of a smoothly bounded, strongly pseudoconvex domain. The estimate is obtained by relating the Bergman kernel to the Neumann operator, and estimating the Neumann operator using certain biholomorphic coordinate changes chosen to take advantage of the boundary geometry. The result obtained says, essentially, that a weight function which is smooth up to the boundary of the domain neither improves nor worsens the singularity of the kernel near the boundary diagonal.