Comparison of the Bergman and Szegö kernels

By Boyong Chen, Siqi Fu. 2010

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Abstract The quotient of the Szego and Bergman kernels for a smooth bounded pseudoconvex domains in C n is bounded from above by a constant multiple of δ | log δ | p 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 δ | log δ | p for any p − 1 . Moreover, for convex domains, the quotient is bounded from above and below by constant multiples of δ.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2ce65a49dce899c4a3602423971cc61a250a6436