AI 中文总结
该研究证明Hardy平均算子的最优Orlicz定义域与最优重排不变定义域重合，提出新泛函提升对偶范数计算性，还得到Hardy-Littlewood极大函数等算子的最优Orlicz空间映射性质。
AI 中文摘要
我们证明，Hardy平均算子可映射到的最大Orlicz空间，与可映射到该空间的最大重排不变（r.i.）空间重合；换言之，最优Orlicz定义域自动成为最优r.i.定义域。更一般地，我们表明每个Luxemburg-Orlicz范数等价于一个次线性泛函，该泛函可提升插值K-理论中出现的对偶范数某表达式的可计算性。作为应用，我们得到Hardy-Littlewood极大函数、逼近恒等式及Calderón-Zygmund奇异积分算子的Orlicz空间映射性质，且这些性质对Hardy-Littlewood极大函数和逼近恒等式而言是最优的。
英文摘要
We prove that the largest Orlicz space into which the Hardy averaging operator maps coincides with the largest rearrangement-invariant (r.i.) space mapping into that space; in other words, the optimal Orlicz domain is automatically the optimal r.i.\ domain. More generally, we show that every Luxemburg--Orlicz norm is equivalent to a sublinear functional which makes more computable a certain expression for a dual norm arising in the $\K$-theory of interpolation. As applications we obtain Orlicz-space mapping properties for the Hardy--Littlewood maximal function, approximate identities and Calderón--Zygmund singular integral operators. These mapping properties are shown to be optimal for the Hardy-Littlewood maximal function and the approximate identities.
Comments16 pages
