Dirichlet-like space and capacity in complex analysis in several variables

Details Dirichlet-like space and capacity in complex analysis in several variables Dirichlet-like space and capacity in complex analysis in several variables

2007-05-22

arxiv.org/abs/0705.3164v1

Mathematics

Complex Variables

29 pages

Scientific paper

For a Kahler manifold X, we study a space of test functions W* which is a complex version of H1. We prove for W* the classical results of the theory of Dirichlet spaces: the functions in W* are defined up to a pluripolar set and the functional capacity associated to W* tests the pluripolar sets. This functional capacity is a Choquet capacity. The space W* is not reflexive and the smooth functions are not dense in it for the strong topology. So the classical tools of potential theory do not apply here. We use instead pluripotential theory and Dirichlet spaces associated to a current.

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