Limiting variants of Krasnosel'skiĭ's compact interpolation theorem

Abstract

We illustrate how limiting variants of Krasnosel'skivı's compact interpolation theorem may be obtained. As a specia lcase of our results it follows that compactness is preserved on certain Lorentz-Zygmund spaces close to the end-point Lebesgue spaces.

Keywords

• Compact operators
• Interpolation
• K-functional
• Type of interpolation method
• Lebesgue spaces
• Lorentz–Zygmund spaces