论文标题
电荷分布和Balayage的Lindelöf条件
The Lindelöf Condition for Charge Distribution and Balayage
论文作者
论文摘要
令$ν$为复杂平面$ \ mathbb c $的充电分配，即$ \ mathbb c $上的真实ra量，总变量$ |ν| $。如果$$ \ limsup_ {0 <r \ to+\ frac} \ frac {1} {t} | v | v | \ bigl（\ bigl \ \ in \ mathb c \ bigm | kigm | kig | $$费用分配$ν$满足属属$ 1 $的条件，如果$$ \ limsup_ {1 \ leq r \ to +\ iffty} \ biggl | \ bigGl | \ int_ \ frac {1} {z} \ operatorAtorname {d} \！ν（z）\ biggr | <+\ infty。 $$，这些概念在研究指数类型的整个功能和有限类型的次谐波功能以及其应用中起着关键作用。在我们以前的作品中，开发了一种有限属$ q = 0,1，\点\点的收费分配$ν$的技术。我们表明，在$ν$的某种情况下，在半平面中保留了这对属性的费用分布$ν$的属的balayage $ q = 1 $。
Let $ν$ be a charge distribution on the complex plane $\mathbb C$, i.e. the real Radon measure on $\mathbb C$ with total variation $|ν|$. The charge distribution $ν$ is of finite upper density under order of $1$ if $$ \limsup_{0<r\to+\infty} \frac{1}{t}|ν|\Bigl(\bigl\{z\in \mathbb C \bigm| |z|\leq r\bigr\}\Bigr)<+\infty. $$ The charge distribution $ν$ satisfies the Lindelöf condition of genus $1$ if $$ \limsup_{1\leq r\to +\infty}\biggl|\int_{1\leq |z|\leq r} \frac{1}{z}\operatorname{d}\!ν(z)\biggr|<+\infty. $$ These concepts play a key role in the study of entire functions of exponential type and subharmonic functions of finite type under order of $1$, as well as in their applications. In our previous works, a technique was developed for balayage of finite genus $q=0,1,\dots$ of the charge distribution $ν$ from the half-plane. We show that balayage of genus $q=1$ of the charge distribution $ν$ from the half-plane preserves this pair of properties under some condition on $ν$.
