发表机构
Université Laval（拉瓦尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究与多马尔一致有界性定理相关的泛函不等式\(f(r + s)\leq g(r)+\alpha f(s)\)，通过给出问题的解，对多马尔定理给出新证明并得到明确界。
AI 中文摘要
我们研究泛函不等式\[ f(r + s)\leq g(r)+\alpha f(s) \quad(r,s>0) \]。其中\(g:(0,\infty)\to[0,\infty)\)是给定的递减函数，\(\alpha\)是满足\(0<\alpha<1\)的常数。问题是确定满足此不等式的递减函数族\(f:(0,\infty)\to[0,\infty)\)是否在\((0,\infty)\)上由某个有限函数有上界，若如此，找出该函数的界。我们给出了此问题的一个解，并用于给出多马尔关于某些次调和函数族一致有界性定理的新证明，还得到了明确的界。
英文摘要
We study the functional inequality \[ f(r+s)\le g(r)+αf(s) \quad(r,s>0). \] Here $g:(0,\infty)\to[0,\infty)$ is a given decreasing function, $α$ is a constant such that $0<α<1$, and the problem is to determine whether the family of decreasing functions $f:(0,\infty)\to[0,\infty)$ that satisfy this inequality is bounded above by some finite function on $(0,\infty)$ and, if so, to find bounds for this function. We present a solution to this problem, and use it to give a new proof of a theorem of Domar on the uniform boundedness of certain families of subharmonic functions, in addition obtaining explicit bounds.
Comments13 pages
