Some extensions of optimal interpolation in spaces of Lorentz-Zygmund type (Q5957341)

Lorentz-Zygmund spaces \(L^{p,r}(\log L)^\alpha\) on \((0,1)\) were introduced by \textit{C. Bennett} and \textit{K. Rudnick} [Diss. Math. 175 (1980; Zbl 0456.46028)], and they obtained an optimal interpolation theorem for quasilinear operators on them. This result refers to Lorentz-Zygmund spaces, but it can be improved when other rearrangement invariant spaces are permitted, as shown by the author [J. Anal. Math. 79, 113-157 (1999; Zbl 0987.46035)] through changing the \(L_r\) norm by the norm of some other rearrangement invariant spaces \(E\) in the definition of Lorentz-Zygmund spaces. In the paper under review, these results on optimal interpolation are extended to the case \(p<1\), to spaces on \((1,\infty)\) and the parameters \(\alpha\) and \(E\) are allowed to change in the interpolation process.