论文标题
洛伦兹 - 卡拉马塔空间
Lorentz--Karamata spaces
论文作者
论文摘要
在本文中，我们考虑了Lorentz-Karamata空间具有缓慢变化的功能，并提供了对其性质的全面研究。 我们考虑使用具有非原子测量和相应的lorentz-karamata空间的任意Sigma-Finite测量空间上的Lorentz-Karamata功能。我们表征了上述空间的非平凡性，然后研究它们等同于Banach功能空间并获得完整的表征。我们计算上述空间的基本功能，并描述相应的端点空间。我们进一步提供了何时使用非进攻重排定义的lorentz-karamata空间的完整表征，相当于使用最大函数定义的空间。我们提供了Lorentz-Karamata空间的副空间的完整描述。我们还对待其他主题，例如嵌入，（准）规范的绝对连续性和Boyd指数。
In this paper, we consider Lorentz--Karamata spaces with slowly varying functions and provide a comprehensive study of their properties. We consider Lorentz--Karamata functionals over an arbitrary sigma-finite measure space equipped with a non-atomic measure and the corresponding Lorentz--Karamata spaces. We characterise non-triviality of said spaces, then study when they are equivalent to a Banach function space and obtain a complete characterisation. We compute the fundamental function of said spaces and describe the corresponding endpoint spaces. We further provide a complete characterisation of when the Lorentz--Karamata spaces defined using non-increasing rearrangement are equivalent to those defined using maximal function. We provide a complete description of the associate spaces of Lorentz--Karamata spaces. We also treat other topics like embeddings, absolute continuity of the (quasi)norm, and Boyd indices.
