Extrapolation functors on a family of scales generated by the real interpolation method

A new class of extrapolation functors is defined on a family of scales generated by the real interpolation method. We prove extrapolation relations for the $\mathscr{K}$- and $\mathscr{J}$-functionals corresponding to some natural pairs of limit spaces which make it possible to describe the values of these functors. We can consider these relations as new assertions similar to the classical Yano theorem on estimates for the norms of operators in interpolation scales of spaces.