Further regularity results in P- extremal setting

Abstract

In our paper, Pluripotential theory and convex bodies: a Siciak-Zaharjuta theorem (Computational Methods and Function Theory (2020), 20(3-4), 571-590) by Bayraktar et al., we proved a regularity result of P-extremal function. In this paper, we prove some other stronger regularity results analogue to those in the standard setting. Specifically we focus on proving the following proposition: Proposition: Let K = Dsubset of C-d be the closure of a bounded domain D with partial derivative D of class C-1,C-1. Then, for any Q is an element of C-alpha(K), where C-alpha(K) is the H & ouml;lder class alpha on K, we have V-P,V-K,V-Q is an element of C-alpha(C-d) for a convex body P subset of(R+)(d).