Disk Envelopes of Functions, II

✍ Scribed by Evgeny A. Poletsky

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 184 KB
• Volume: 163
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1998.3378

✦ Synopsis

Given a Suslin function , on a domain Y in a Banach space X one can define two envelopes of , related to the pluripotential theory. The first one, denoted by P,, is the supremum of all plurisubharmonic functions less than ,. The value of the other one, denoted by D ,, at some point z is equal to the infimum of integrals over the boundaries of all closed analytic disks centered at z. In this paper we study the relationship between these envelopes. We show that D , P*, for a large class of functions on domains in Banach spaces, where P*, is the upper regularization of P,. If X=C n , then we prove that D *, is always equal to P*,.