TY - JOUR
T1 - Disk Envelopes of Functions, II
AU - Poletsky, Evgeny A.
N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 1999/4/1
Y1 - 1999/4/1
N2 - Given a Suslin functionφon a domainYin a Banach spaceXone can define two envelopes ofφrelated to the pluripotential theory. The first one, denoted byPφ, is the supremum of all plurisubharmonic functions less thanφ. The value of the other one, denoted byDφ, at some pointzis equal to the infimum of integrals over the boundaries of all closed analytic disks centered atz. In this paper we study the relationship between these envelopes. We show thatDφ≤P*φfor a large class of functions on domains in Banach spaces, whereP*φis the upper regularization ofPφ. IfX=Cn, then we prove thatD*φis always equal toP*φ.
AB - Given a Suslin functionφon a domainYin a Banach spaceXone can define two envelopes ofφrelated to the pluripotential theory. The first one, denoted byPφ, is the supremum of all plurisubharmonic functions less thanφ. The value of the other one, denoted byDφ, at some pointzis equal to the infimum of integrals over the boundaries of all closed analytic disks centered atz. In this paper we study the relationship between these envelopes. We show thatDφ≤P*φfor a large class of functions on domains in Banach spaces, whereP*φis the upper regularization ofPφ. IfX=Cn, then we prove thatD*φis always equal toP*φ.
KW - Pluripotential theory
KW - Plurisubharmonic functions
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U2 - 10.1006/jfan.1998.3378
DO - 10.1006/jfan.1998.3378
M3 - Article
AN - SCOPUS:0001022319
VL - 163
SP - 111
EP - 132
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
ER -