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

C.P. Calderón, A. Torchinsky

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