论文标题
亚谐波功能的积分及其在射线上的小集合上的重量的差异
Integrals of subharmonic functions and their differences with weight over small sets on a ray
论文作者
论文摘要
让$ e $成为一个段$ [0，r] $的可测量子集，在复杂平面中的正轴的积极部分，而$ u = u-v $是subharmonic函数$ u \ u \ equiv-equiv-equiv-equiv-equiv-equiv-equiv-equiv-equiv-equiv-equiv $ and $ v \ not \ equiv- equiv- equiv- \ equiv- \ equiv- \ eftty $。圆圈上的最大值，以$ u^+：= \ sup \ {0，u \} $或$ | u | $ over $ e $上的$ multiplier $ g \ in l^p（e）$ in l^p（e）$ in l^p（e）$ conterial the Ligational of $ u $ $ u $ u $ u $ u Circe cirde conde，$ u $ u $ u $ u $ u $ u $ u $ u $ u $ u $ u $ g \ $ e $的lebesgue量度和$ g $的$ l^p $ norm。我们的主要定理制定了Rolf Nevanlinna的经典定理之一的证明，在$ e = [0，r] $中，由Anatolii A. Gol'dberg和Iosif V. ostrovskii在经典专着中给出，并且还将eDrei-fuchuchs lemma的类似物的类似物属于小型A. Sodin，T.I。 Malyutina。我们的估计值是统一的，因为这些估算中的常数不取决于$ u $或$ u $，但前提是$ u $分别在零接近零或$ u（0）\ geq 0 $的整体标准化。
Let $E$ be a measurable subset in a segment $[0,r]$ in the positive part of the real axis in the complex plane, and $U=u-v$ be the difference of subharmonic functions $u\not\equiv -\infty$ and $v\not\equiv-\infty$ on the complex plane. An integral of the maximum on circles centered at zero of $U^+:=\sup\{0,U\} $ or $|u|$ over $E$ with a function-multiplier $g\in L^p(E)$ in the integrand is estimated, respectively, in terms of the characteristic function $T_U$ of $U$ or the maximum of $u$ on circles centered at zero, and also in terms of the linear Lebesgue measure of $E$ and the $ L^p$-norm of $g$. Our main theorem develops the proof of one of the classical theorems of Rolf Nevanlinna in the case $E=[0,R]$, given in the classical monograph by Anatolii A. Gol'dberg and Iosif V. Ostrovskii, and also generalizes analogs of the Edrei-Fuchs Lemma on small arcs for small intervals from the works of A.F. Grishin, M.L. Sodin, T.I. Malyutina. Our estimates are uniform in the sense that the constants in these estimates do not depend on $U$ or $u$, provided that $U$ has an integral normalization near zero or $u(0)\geq 0$, respectively.
