On extrapolation blowups in the $L_p$ scale

Yano's extrapolation theorem dated back to 1951 establishes boundedness properties of a subadditive operator acting continuously in for close to and/or taking into as and/or with norms blowing up at speed and/or,. Here we give answers in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces to what happens if as. The study has been motivated by current investigations of convolution maximal functions in stochastic analysis, where the problem occurs for . We also touch the problem of comparison of results in various scales of spaces.