Almost-compact embeddings

作者：Slavikova Lenka^*

来源：Mathematische Nachrichten, 2012, 285(11-12): 1500-1516.

DOI：10.1002/mana.201100286

• Almost-compact embedding
• Banach function space
• rearrangement-invariant space
• product operator
• almost-everywhere convergence
• Lorentz endpoint space
• Marcinkiewicz endpoint space
• msc (2010) 46E30

We study almost-compact embeddings between Banach function spaces. We prove a necessary and sufficient condition in terms of almost-everywhere convergence. We also study the dependence of an almost-compact embedding on the measure space. We introduce a certain product operator and show its intimate relation to an almost-compact embedding. We also characterize general almost-compact embeddings among Lorentz and Marcinkiewicz endpoint spaces.

• 出版日期2012-8