Plurisubharmonic and holomorphic functions relative to the plurifine topology

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

A weak and a strong concept of plurifinely plurisubharmonic and plurifinely holomorphic functions are introduced. Strong will imply weak. The weak concept is studied further. A function f is weakly plurifinely plurisubharmonic if and only if it is locally bounded from above in the plurifine topology and f∘h is finely subharmonic for all complex affine-linear maps h. As a consequence, the regularization in the plurifine topology of a pointwise supremum of such functions is weakly plurifinely plurisubharmonic, and it differs from the pointwise supremum at most on a pluripolar set. Weak plurifine plurisubharmonicity and weak plurifine holomorphy are preserved under composition with weakly plurifinely holomorphic maps.
TidsskriftJournal of Mathematical Analysis and Applications
Udgave nummer2
Sider (fra-til)706-723
StatusUdgivet - 2011

ID: 37567709