Some New Extrapolation Estimates for the Scale of Spaces

Abstract

Using new extrapolation estimates for the \(K\)- and \(J\)-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.