Comparison of the Bergman and Szegö kernels

The quotient of the Szegö and Bergman kernels for a smooth bounded pseudoconvex domains in Cn is bounded from above by a constant multiple of δ|logδ|p for any p>n, where δ is the distance to the boundary. For a class of domains that includes those of D'Angelo finite type and those with plurisubharmonic defining functions, the quotient is also bounded from below by a constant multiple of δ|logδ|p for any p<-1. Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.