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1
Content available remote

The symmetric pluricomplex Green function

100%
Cegrell U.
Banach Center Publications
|
1995
|
tom 31
|
nr 1
135-141
2
Content available remote

Potentials with respect to the pluricomplex Green function

100%
Cegrell U.
Annales Polonici Mathematici
|
2012
|
tom 106
|
nr 1
107-111
EN
For μ a positive measure, we estimate the pluricomplex potential of μ, $P_{μ}(x) = ∫_{Ω} g(x,y) dμ(y)$, where g(x,y) is the pluricomplex Green function (relative to Ω) with pole at y.
3
Content available remote

A general Dirichlet problem for the complex Monge-Ampère operator

100%
Cegrell U.
Annales Polonici Mathematici
|
2008
|
tom 94
|
nr 2
131-147
EN
We study a general Dirichlet problem for the complex Monge-Ampère operator, with maximal plurisubharmonic functions as boundary data.
4
Content available remote

On the spectrum of A(Ω) and $H^∞(Ω)$

100%
Cegrell U.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 2
193-199
EN
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.
5
Content available remote

The gradient lemma

100%
Cegrell U.
Annales Polonici Mathematici
|
2007
|
tom 91
|
nr 2-3
143-146
EN
We show that if a decreasing sequence of subharmonic functions converges to a function in $W_{loc}^{1,2}$ then the convergence is in $W_{loc}^{1,2}$.
6
Content available remote

Extremal plurisubharmonic functions

64%
Cegrell U., Thorbiörnson J.
Annales Polonici Mathematici
|
1996
|
tom 63
|
nr 1
63-69
EN
We study different notions of extremal plurisubharmonic functions.
7
Content available remote

An energy estimate for the complex Monge-Ampère operator

64%
Cegrell U., Persson L.
Annales Polonici Mathematici
|
1997
|
tom 67
|
nr 1
95-102
EN
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.
8
Content available remote

Monge-Ampère boundary measures

64%
Cegrell U., Kemppe B.
Annales Polonici Mathematici
|
2009
|
tom 96
|
nr 2
175-196
EN
We study swept-out Monge-Ampère measures of plurisubharmonic functions and boundary values related to those measures.
9
Content available remote

Jensen measures, hyperconvexity and boundary behaviour of the pluricomplex Green function

52%
Carlehed M., Cegrell U., Wikström F.
Annales Polonici Mathematici
|
1999
|
tom 71
|
nr 1
87-103
EN
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.
10
Content available remote

Spectrum of certain Banach algebras and ∂̅-problems

52%
Carlsson L., Cegrell U., Fällström A.
Annales Polonici Mathematici
|
2007
|
tom 90
|
nr 1
51-58
EN
We study the spectrum of certain Banach algebras of holomorphic functions defined on a domain Ω where ∂̅-problems with certain estimates can be solved. We show that the projection of the spectrum onto ℂⁿ equals Ω̅ and that the fibers over Ω are trivial. This is used to solve a corona problem in the special case where all but one generator are continuous up to the boundary.
11
Content available remote

On the domains of existence for plurisubharmonic functions

44%
Cegrell U.
Banach Center Publications
|
1983
|
tom 11
|
nr 1
33-37
12
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Small sets in $C^n$

32%
Cegrell U.
Annales Polonici Mathematici
|
1985
|
tom 46
|
nr 1
55-60
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