# Diagonal Estimates for Bergman Kernels in Monomial-Type Domains

# Diagonal Estimates for Bergman Kernels in Monomial-Type Domains

This chapter discusses diagonal estimates for Bergman kernels in monomial-type domains. It begins by briefly recalling the definition and some of the elementary properties of the Bergman projection and Bergman kernel. The chapter then turns to a problem which requires obtaining uniform estimates for a Bergman kernel on the diagonal of a model monomial domain. The chapter then sketches an approach devised by Gregor Herbort in 1983, when he gave an example in which the growth of the Bergman kernel on the diagonal is not given by a negative power of the distance to the boundary. Through Herbort's method, the chapter arrives at its required estimates.

*Keywords:*
Bergman kernels, model monomial domain, monomial-type domains, diagonal estimates, Bergman projection, Gregor Herbort