Description of K-spaces by means of J-spaces and the reverse problem in the limiting real interpolation

Abstract

We establish conditions under which K-spaces in the limiting real interpolation involving slowly varying functions can be described by means of J-spaces and we also solve the reverse problem. To this end, we prove several versions of the fundamental lemma of the real interpolation theory.

We apply our results to obtain density theorems for the corresponding limiting interpolation spaces.

Keywords

• density theorems
• fundamental lemmas
• J-method
• K-method
• limiting real interpolation
• slowly varying functions
• weighted inequalities
• weighted Lebesgue spaces