A Generalization of the Corona Theorem in the Unit Disc.
Some Characterizations of L-regular Points.
A Local Property of L-regular Sets.
On the Dirichlet Problem for the Complex Monge-Ampère Operator.
Sums of Continuous Plurisubharmonic Functions and the Complex Monge-Ampère Operator in ....n.
Delta-plusharmonic functions.
On the domains of existence for plurisubharmonic functions
The symmetric pluricomplex Green function
On the spectrum of A(Ω) and
We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.
Small sets in
On ideals generated by bounded analytic functions in the bidisc
The general definition of the complex Monge-Ampère operator
We define and study the domain of definition for the complex Monge-Ampère operator. This domain is the most general if we require the operator to be continuous under decreasing limits. The domain is given in terms of approximation by certain " test"-plurisubharmonic functions. We prove estimates, study of decomposition theorem for positive measures and solve a Dirichlet problem.
The gradient lemma
We show that if a decreasing sequence of subharmonic functions converges to a function in then the convergence is in .
A general Dirichlet problem for the complex Monge-Ampère operator
We study a general Dirichlet problem for the complex Monge-Ampère operator, with maximal plurisubharmonic functions as boundary data.
Potentials with respect to the pluricomplex Green function
For μ a positive measure, we estimate the pluricomplex potential of μ, , where g(x,y) is the pluricomplex Green function (relative to Ω) with pole at y.
On the space and dual space of functions representable by differences of subharmonic functions
Extremal plurisubharmonic functions
We study different notions of extremal plurisubharmonic functions.
An energy estimate for the complex Monge-Ampère operator
We prove an energy estimate for the complex Monge-Ampère operator, and a comparison theorem for the corresponding capacity and energy. The results are pluricomplex counterparts to results in classical potential theory.
Monge-Ampère boundary measures
We study swept-out Monge-Ampère measures of plurisubharmonic functions and boundary values related to those measures.
Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function
We characterise hyperconvexity in terms of Jensen measures with barycentre at a boundary point. We also give an explicit formula for the pluricomplex Green function in the Hartogs triangle. Finally, we study the behaviour of the pluricomplex Green function g(z,w) as the pole w tends to a boundary point.
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