23 citations · 50 across the 11 of their papers we have counts for
13 papers
On the regularity of the complex Hessian equation
Per Ahag, Rafal Czyz
This note aims to investigate the regularity of a solution to the Dirichlet problem for the complex Hessian equation, which has a density of the -Hessian measure that belongs to…
On a family of quasimetric spaces in generalized potential theory
Per Ahag, Rafal Czyz
We construct a family of quasimetric spaces in generalized potential theory containing -subharmonic functions with finite -energy. These quasimetric spaces will be viewed…
Geodesics in the space of -subharmonic functions with bounded energy
Per Ahag, Rafal Czyz
With inspiration from the Kähler geometry, we introduce a metric structure on the energy class, , of -subharmonic functions with bounded energy and show that…
A characterization of the degenerate complex Hessian equations for functions with bounded -energy
Per Ahag, Rafal Czyz
By proving an estimate of the sublevel sets for -subharmonic functions we obtain a Sobolev type inequality that is then used to characterize the degenerate complex Hessian e…
Poincaré- and Sobolev- type inequalities for complex -Hessian equations
Per Ahag, Rafal Czyz
By using quasi-Banach techniques as key ingredient we prove Poincaré- and Sobolev- type inequalities for -subharmonic functions with finite -energy. A consequence of the…
The Dirichlet problem for -subharmonic functions on compact sets
Per Ahag, Rafal Czyz, Lisa Hed
We characterize those compact sets for which the Dirichlet problem has a solution within the class of continuous -subharmonic functions defined on a compact set, and then within…
On the Moser-Trudinger inequality in complex space
Per Ahag, Rafal Czyz
In this paper we prove the pluricomplex counterpart of the Moser-Trudinger and Sobolev inequalities in complex space. We consider these inequalities for plurisubharmonic functions…
The classification of holomorphic --subharmonic morphisms
Per Ahag, Rafal Czyz, Lisa Hed
We study the problem of classifying the holomorphic -subharmonic morphisms in complex space. This determines which holomorphic mappings preserves -subharmonicity in the s…
Extension and approximation of -subharmonic functions
Per Ahag, Rafal Czyz, Lisa Hed
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 cha…
The geometry of -hyperconvex domains
Per Ahag, Rafal Czyz, Lisa Hed
We study the geometry of -regular domains within the Caffarelli-Nirenberg-Spruck model in terms of barrier functions, envelopes, exhaustion functions, and Jensen measures. We pr…
On Dirichlet's principle and problem
Per Ahag, Urban Cegrell, Rafal Czyz
The aim of this paper is to give a new proof of the complete characterization of measures for which there exist a solution of the Dirichlet problem for the complex Monge-Ampere ope…
On a Monge-Ampère type equation in the Cegrell class
Rafał Czyż
In this paper we prove an existence and uniqueness result for a Monge-Ampère type equation in the Cegrell class .
Monge-Ampere measures on pluripolar sets
Per Ahag, Urban Cegrell, Rafal Czyz +1
In this article we solve the complex Monge-Ampere equation for measures with large singular part. This result generalizes classical results by Demailly, Lelong and Lempert a.o., wh…