On the equivalence of the Lorentz and Marcinkiewicz norm on subsets of measurable functions (Q1188103)

Given a measurable function \(x\) on (0,1) we denote by \(x_ n\) the function \[ x_ n(t)=\begin{cases} x(t) & \text{ if } | x(t)|\leq n \\ n\text{ sign} x(t) & \text{ if } | x(t)|>n. \end{cases} \] The authors characterize sets of measurable functions for which sequences \((x_ n)^ \infty_{n=1}\) have equivalent Lorentz and Marcinkiewicz norms.