Equivalence of \(K\)- and \(J\)-methods for limiting real interpolation spaces (Q647634)

The aim of this paper is to give an equivalence theorem between real interpolation spaces using the \(J\)-method and those using the \(K\)-method. (See Theorem 4.7.) This theorem was known in the case \(0<\theta <1,\) but certain questions in function spaces have motivated the investigation of the limiting real interpolation spaces. These limiting real interpolation spaces including logarithmic terms in their definition are considered in the present paper and Theorem 4.7 is proved for them. The motivation to obtain such a result consists in applications to approximation of stochastic integrals. (See Section 5.)