Some New Extrapolation Estimates for the Scale of $L_p$-Spaces

Using new extrapolation estimates for the $\mathcal{K}$- and $\mathcal{J}$-functionals of couples of limit spaces of the $L_p$-scale ($1<p<\infty$), we introduce a class of extrapolation functors. A characterization of this class via the real interpolation method permits one to obtain new equivalent expressions for the norms in symmetric spaces “close” to $L_\infty$ and $L_1$, which depend only on the $L_p$-norms of a function.