有限模和的调和逼近
Harmonic approximation by finite sums of moduli
摘要：
令$h(B_d)$表示$\mathbb{R}^d$的单位球$B_d$上的实值调和函数空间，$d\ge 2$。给定$B_d$上的径向权$w$，考虑以下问题：在$h(B_d)$中构造有限族$\{f_1, f_2, \dots, f_J\}$，使得和$|f_1| + |f_2|+\dots + |f_J|$等价于$w$。我们解决了问题的权重$w$的加倍属性。此外，如果$d$是甚至，那么我们的特点是这些$w$的问题有一个解决方案。
英文摘要：
Let $h(B_d)$ denote the space of real-valued harmonic functions on the unit ball $B_d$ of $\mathbb{R}^d$, $d\ge 2$. Given a radial weight $w$ on $B_d$, consider the following problem: construct a finite family $\{f_1, f_2, \dots, f_J\}$ in $h(B_d)$ such that the sum $|f_1| + |f_2|+\dots + |f_J|$ is equivalent to $w$. We solve the problem for weights $w$ with a doubling property. Moreover, if $d$ is even, then we characterize those $w$ for which the problem has a solution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
