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

Authors

  • Calixto Calderón Dept of Math, Stat & Comp Sci, University of Illinois at Chicago, Chicago IL 60607, USA
  • Alberto Torchinsky Dept of Math, Indiana University, Bloomington IN 47405, USA

DOI:

https://doi.org/10.33044/revuma.1861

Abstract

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].

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Published

2021-05-21

Issue

Vol. 62 No. 1 (2021)

Section

Article

License

Copyright (c) 2021 Alberto Torchinsky

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