19 research outputs found
Extension and approximation of -subharmonic functions
Let be a bounded domain, and let be a
real-valued function defined on the whole topological boundary . The aim of this paper is to find a characterization of the functions
which can be extended to the inside to a -subharmonic function under
suitable assumptions on . We shall do so by using a function algebraic
approach with focus on -subharmonic functions defined on compact sets. We
end this note with some remarks on approximation of -subharmonic functions
Weighted pluricomplex energy
We study the complex Monge-Ampre operator on the classes of finite
pluricomplex energy in the general case
( i.e. the total Monge-Ampre mass may be infinite). We establish an
interpretation of these classes in terms of the speed of decrease of the
capacity of sublevel sets and give a complete description of the range of the
operator on the classes Comment: Contrary to what we claimed in the previous version, in Theorem 5.1
we generalize some Theorem of Urban Cegrell but we do not give a new proof.
To appear in Potenial Analysi
Partial pluricomplex energy and integrability exponents of plurisubharmonic functions
We give a sufficient condition on the Monge-Amp\`ere mass of a
plurisubharmonic function for to be locally integrable. This
gives a pluripotential theoretic proof of a theorem by J-P. Demailly.Comment: extended version with new results and more application