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

Abstract

We describe the Lorentz space $L(p,r),0<r<p,p>1$, in terms of Orlicz type classes of functions L . As a consequence of this result it follows that Stein's characterization of the real functions on $R^n$ that are differentiable at almost all the points in $R^n$, is equivalent to the earlier characterization of those functions given by A. P. Calderon.