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 for any p>n, where δ is the distance to the boundary. For a class of domains that includes those of DʼAngelo finite type and those with plurisubharmonic defining functions, the quotient is also bounded from below by a constant multiple of for any p<−1. Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.