论文标题
关于该点在无穷大的作用中，否认质量对Riesz电位的阳性原理
On the role of the point at infinity in Deny's principle of positivity of mass for Riesz potentials
论文作者
论文摘要
首先由J. Deny提出，大规模阳性的经典原则指出，如果$ \ \ \ \ \ m athbb {r}^n $，则为$κ_αμ\leqslantκ_αν$，则是$ \ mathbb {r}^n $，则是$μ（\ mathbb {r}^n）\ leqslantNantN $这里$μ，ν$是$ \ mathbb {r}^n $，$ n \ geqslant2 $的积极措施，而$κ__αμ$对于Riesz kernel $ | | x-y | x-y |^{α-n} $ in（0,0,2] $ a $ riesz kernel $ | x-y |^α-n} $的可能性，$ | $μ（\ Mathbb {r}^n）\leqslantν（\ m athbb {r}^n）$仍然容易成立因此。 Riesz平衡度量（潜在的肛门，2022年），在能量和总质量都可以无限的情况下，在扩展的意义上可以理解内部平衡度量。
First introduced by J. Deny, the classical principle of positivity of mass states that if $κ_αμ\leqslantκ_αν$ everywhere on $\mathbb{R}^n$, then $μ(\mathbb{R}^n)\leqslantν(\mathbb{R}^n)$. Here $μ,ν$ are positive Radon measures on $\mathbb{R}^n$, $n\geqslant2$, and $κ_αμ$ is the potential of $μ$ with respect to the Riesz kernel $|x-y|^{α-n}$ of order $α\in(0,2]$, $α<n$. We strengthen Deny's principle by showing that $μ(\mathbb{R}^n)\leqslantν(\mathbb{R}^n)$ still holds even if $κ_αμ\leqslantκ_αν$ is fulfilled only on a proper subset $A$ of $\mathbb{R}^n$ that is not inner $α$-thin at infinity; and moreover, this condition on $A$ cannot in general be improved. Hence, if $ξ$ is a signed measure on $\mathbb{R}^n$ with $\int1\,dξ>0$, then $κ_αξ>0$ everywhere on $\mathbb{R}^n$, except for a subset which is inner $α$-thin at infinity. The analysis performed is based on the author's recent theories of inner Riesz balayage and inner Riesz equilibrium measures (Potential Anal., 2022), the inner equilibrium measure being understood in an extended sense where both the energy and the total mass may be infinite.
