2 citations · 2 across the 4 of their papers we have counts for
10 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…