Boundary behavior of the Kobayashi metric near a point of infinite type

Under a potential-theoretical hypothesis named $f$-Property with $f$ satisfying $\displaystyle\int_t^\infty \dfrac{da}{a f(a)}<\infty$, we show that the Kobayashi metric $K(z,X)$ on a weakly pseudoconvex domain \Om, satisfies the estimate K(z,X)\ge Cg(\delta_\Om(x)^{-1})|X| for any X\in T^{1,0}\Om where $(g(t))^{-1}$ denotes the above integral and \delta_\Om(z) is the distance from $z$ to b\Om.Comment: 15 page

Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type

The purpose of this paper is to prove $L^p$-Sobolev and H\"older estimates for the Bergman projection on a class of pseudoconvex domains that admit a "good" dilation and satisfy Bell-Ligocka's Condition R. We prove that this class of domains includes the $h$-extendible domains, a large class of weakly pseudoconvex domains of finite type.Comment: 15 pages. We corrected a substantial error in the Application section from the previous versio