2020/06/25 by Dalimil Peša, Peša, Dalimil · 2 citations
Mathematics · #46E30 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2006.14455
openalex publication_date 2020/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.