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arXiv · 1011.4472

Plurisubharmonic and holomorphic functions relative to the plurifine topology

Mohamed El Kadiri·Bent Fuglede·Jan Wiegerinck
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Abstract

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 f o 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.

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Mohamed El Kadiri, Bent Fuglede, Jan Wiegerinck. 2010-11-19. Plurisubharmonic and holomorphic functions relative to the plurifine topology. https://arxiv.org/abs/1011.4472

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