相关论文: Weighted energy class of $m$-subharmonic functions

In this paper we study the class $\mathcal{E}_{m}(\Omega)$ of $m-$subharmonic functions introduced by Lu in \cite{L1}. We prove that the convergence in $m-$capacity implies the convergence of the associated Hessian measure for functions…

In this paper, we concern with the existence of solutions of the complex $m-$Hessian type equation $-\chi(u)H_{m}(u)=\mu$ in the class $\mathcal{E}_{m,\chi}(f,\Omega)$ if there exists subsolution in this class, where the given boundary…

In this paper, we concern with the existence of solutions of the weighted complex $m$-Hessian equation $-\chi(u)H_{m}(u)=\mu$ in the class $\mathcal{E}_{m,\chi}(f,\Omega)$ if there exists subsolution in this class, where the given boundary…

In this paper we establish a result on subextension of $m$-subharmonic functions in the class $\mathcal{F}_m(\Omega,f)$ without changing the hessian measures. As application, we approximate a $m$-subharmonic function with given boudary…

In this paper, we first study subextensions in the classes $\mathcal{F}_{m}(\Omega)$ and $\mathcal{E}_{m,\chi}(\Omega)$. These results are then used to study approximation in the classes $\mathcal{F}_{m}(\Omega)$ and…

We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…

In this article, we investigate the weighted $m-$subharmonic functions. We shall give some properties of this class and consider its relation to the $m-$Cegrell classes. We also prove an integration theorem and an almost everywhere…

Let $1\leq m\leq n$ be two fixed integers. Let $\Omega \Subset \mathbb C^n$ be a bounded $m$-hyperconvex domain and $\mathcal A \subset \Omega \times ]0,+ \infty[$ a finite set of weighted poles. We define and study properties of the…

We introduce a new class $\mathcal{FV}(\Omega,E)$ of spaces of weighted functions on a set $\Omega$ with values in a locally convex Hausdorff space $E$ which covers many classical spaces of vector-valued functions like continuous, smooth,…

In this paper, we first study the definition and the continuity of the complex Hessian operator associated to an $m$-positive closed current $T$, for some classes of unbounded $m$-subharmonic functions as well as when we consider a…

In this paper, we study Hessian type equations for $m-\omega$ subharmonic functions. Using the recent results in \cite{KN23a}, \cite{KN23b}, we are able to show the existence of bounded solutions for such equations on bounded domains in…

In this paper we study the relation between the weighted energy class $\mathcal{E}_{\chi}$ introduced by S. Benelkouchi, V. Guedj and A. Zeriahi recently with the classes $\mathcal{E}$ and $\mathcal{N}$ studied by Cegrell. Moreover, we…

Let $\Omega$ be a $m$-hyperconvex domain of $\mathbb{C}^n$ and $\beta$ be the standard K\"{a}hler form in $\mathbb{C}^n$. We introduce finite energy classes of $m$-subharmonic functions of Cegrell type, $\mathcal{E}_m^p, p>0$ and…

The aim of this paper is to study Capacities and Hessians in a class of m-subharmonic functions

By proving an estimate of the sublevel sets for $(\omega,m)$-subharmonic functions we obtain a Sobolev type inequality that is then used to characterize the degenerate complex Hessian equations for such functions with bounded…

In this paper, we first study the comparison principle for the operator $H_{\chi,m}$. This result is used to solve certain weighted complex $m-$ Hessian equations.

In this paper, we establish the weak*-convergence of a sequence of the complex Hessian measures $H_m(u_j)$ to the complex Hessian measure $H_m(u)$ in the class $\mathcal{E}(X,\omega,m)$ under hypotheses that $u_j$ is convergent to $u$ in…

Let $\Omega\subset \mathbb C^n$ be a bounded domain, and let $f$ be a real-valued function defined on the whole topological boundary $\partial \Omega$. The aim of this paper is to find a characterization of the functions $f$ which can be…

Let $(X,\omega)$ be a compact K\"ahler manifold of dimension $n$ and fix $1\leq m\leq n$. We prove that the total mass of the complex Hessian measure of $\omega$-$m$-subharmonic functions is non-decreasing with respect to the singularity…

Let $\Omega$ be a bounded strictly $m$-pseudoconvex domain of $\mathbb{C}^n$. We solve degenerate complex Hessian equations of the form $(\omega + dd^c \varphi)^m\wedge\beta^{n-m} = \mu$ in the generalized Cegrell classes…