Stability and localization of the Lp Bergman kernel

The aims of this paper are twofold. First, we generalize the classical Ramadanov theorem and Skwarczyński theorem for the Formula: see text Bergman kernels to the Formula: see text case, which are concerned with the compact convergence of Formula: see text Bergman kernels on an increasing or decreasing sequence of domains in Formula: see text. Second, we prove a localization principle for the Formula: see text Bergman kernel on bounded strongly pseudoconvex domains with smooth boundary. Utilize the localization, we study the asymptotic behavior of the Formula: see text Bergman kernel near strongly pseudoconvex boundary points and show that the Formula: see text-Schwarz content is identical to Formula: see text on a neighborhood of a strongly pseudoconvex boundary point.