Revista de la
Unión Matemática Argentina
A characterization of the Lorentz space $L(p,r)$ in terms of Orlicz type classes
Calixto P. Calderón and Alberto Torchinsky
Volume 62, no. 1 (2021), pp. 117–122

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We describe the Lorentz space $L(p,r)$, $0 < r < p$, $p > 1$, in terms of Orlicz type classes of functions $L_{\Psi}$. As a consequence of this result it follows that Stein's characterization of the real functions on $\mathbb{R}^n$ that are differentiable at almost all the points in $\mathbb{R}^n$ [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].