论文标题
年轻功能的家族和规范的限制
Families of Young Functions and Limits of Orlicz Norms
论文作者
论文摘要
给定$σ$ -Finite Measuite Space $（X，μ）$，Young函数$φ$和一个单参数的年轻函数家族$ \ {ψ_Q\} $，我们为任何功能$ f \ in L^φ（x，X，μ）$ f \ [ \ lim_ {q \ rightarrow \ infty} \ | f \ | _ {l^{ψ_q}（x，x，μ）} = c \ | f \ | _ {l^\ infty（x，us）}。 \]常数$ c $独立于$ f $，仅取决于$ \ {ψ_q\} $。在我们的条件失败时，给出了一些满足我们条件的年轻功能的单参数家族的例子。
Given a $σ$-finite measure space $(X,μ)$, a Young function $Φ$, and a one-parameter family of Young functions $\{Ψ_q\}$, we find necessary and sufficient conditions for the associated Orlicz norms of any function $f\in L^Φ(X,μ)$ to satisfy \[ \lim_{q\rightarrow \infty}\|f\|_{L^{Ψ_q}(X,μ)}=C\|f\|_{L^\infty(X,μ)}. \] The constant $C$ is independent of $f$ and depends only on the family $\{Ψ_q\}$. Several examples of one-parameter families of Young functions satisfying our conditions are given, along with counterexamples when our conditions fail.
