AI 中文总结
本文针对 Wiener–Luxemburg 融合空间仅适用于重排不变空间的问题，构建通用框架将其拓展至任意拟Banach函数空间，构造新型拟范数解决结构难题并完成相关性质刻画。
AI 中文摘要
近期提出的 Wiener–Luxemburg 融合空间因过度依赖非增重排，仅适用于重排不变空间的情形。为突破这一限制，本文构建了一套全新的通用框架，将这类融合结构拓展至任意拟Banach函数空间。通过基于测度约束上确界与下确界构造新型拟范数，成功使该类融合空间脱离重排理论的束缚；在该广义框架下，解决了 Fatou 性质相关的结构难题，证明其与原有理论的一致性，且完整刻画了伴随空间、连续嵌入以及范数的绝对连续性。
英文摘要
The fundamental reliance on nonincreasing rearrangements restricts the recently introduced Wiener--Luxemburg amalgam spaces only to the rearrangement-invariant setting. To overcome this barrier, we develop a novel comprehensive framework that expands these amalgam structures to arbitrary quasi-Banach function spaces. By constructing a new quasinorm based on measure-constrained suprema and infima, we successfully separate these amalgams from rearrangement theory. We resolve the ensuing structural challenges regarding the Fatou property in this generalized setting, show consistency with the original theory, and fully characterize associate spaces, continuous embeddings, and the absolute continuity of the norm.
