论文标题
Riesz的Lumer hardy空间定理
Riesz's Theorem for Lumer's Hardy Spaces
论文作者
论文摘要
在本说明中，我们获得了众所周知的Riesz定理的版本，用于Lumer的Hardy Space $（lh）^2（ω）$ $ω$的谐谐波函数：如果真实价值的谐波函数$ u \ u \ u \ u \ u \ in（lh）^2（ω） iv $在$ω$上进行了分析，然后$ u+iv $也属于$（lh）^2（ω）$，对于归一化的偶联，我们具有规范估计$ \ | U+IV \ | _____ {（lh）^2（ω）^2（ω）}以最好的常数。
In this note we obtain a version of the well-known Riesz's theorem on conjugate harmonic functions for Lumer's Hardy spaces $(Lh)^2(Ω)$ on arbitrary domains $Ω$: If a real-valued harmonic function $U\in (Lh)^2(Ω)$ has a harmonic conjugate $V$ on $Ω$ (i.e., a real-valued harmonic function such that $U+ iV$ is analytic on $Ω$), then $U+iV$ also belongs to $(Lh)^2(Ω)$, and for the normalized conjugate we have the norm estimate $\|U+iV\|_{(Lh)^2(Ω)}\le\sqrt{2} \|U\|_{(Lh)^2(Ω)}$, with the best possible constant.
