A characterization of the Lorentz space $L(p,r)$ in terms of Orlicz type classes

We describe the Lorentz space L(p, r), 0 1, in terms of Orlicz type classes functions LΨ. As a consequence this result it follows that Stein’s characterization real on Rn are differentiable at almost all points [Ann. Math 113 (1981), no. 2, 383–385], is equivalent to those given by A. P. Calderon [Riv. Mat. Univ. Parma 2 (1951), 203–213].