Cauchy-Stieltjes integrals on strongly pseudoconvex domains
Let L(z) be the Lie norm on and L*(z) the dual Lie norm. We denote by the space of complex harmonic functions on the open Lie ball and by the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.
A statement in the paper “Holomorphic Morse inequalities on manifolds with boundary” saying that the holomorphic Morse inequalities for an hermitian line bundle over are sharp as long as extends as semi-positive bundle over a Stein-filling is corrected, by adding certain assumptions. A more general situation is also treated.
Some representations of Nash functions on continua in ℂ as integrals of rational functions of two complex variables are presented. As a simple consequence we get close relations between Nash functions and diagonal series of rational functions.
In this paper, we give precise isotropic and non-isotropic estimates for the Bergman and Szegö projections of a bounded pseudoconvex domain whose boundary points are all of finite type and with locally diagonalizable Levi form. Additional local results on estimates of invariant metrics are also given.