The Equivalence Theorem for Logarithmic Interpolation Spaces in the Quasi-Banach Case

Abstract

. We study the description by means of the J -functional of logarithmic interpolation spaces ( A 0 ; A 1 ) 1;q;A in the category of the p -normed quasi-Banach couples (0 < p (cid:20) 1). When ( A 0 ; A 1 ) is a Banach couple, it is known that the description changes depending on the relationship between q and A. In our more general setting, the parameter p also has an important role as the results show.