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On the spectrum of A(Ω) and H ( Ω )

Urban Cegrell — 1993

Annales Polonici Mathematici

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.

The general definition of the complex Monge-Ampère operator

Urban Cegrell — 2004

Annales de l’institut Fourier

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

Urban Cegrell — 2007

Annales Polonici Mathematici

We show that if a decreasing sequence of subharmonic functions converges to a function in W l o c 1 , 2 then the convergence is in W l o c 1 , 2 .

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