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

• C.P. Calderón ^[1] ; A. Torchinsky ^[2]
  1. [1] University of Illinois at Chicago

     University of Illinois at Chicago

     City of Chicago, Estados Unidos

     
  2. [2] Indiana University, USA
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 1, 2021, págs. 117-122
• Idioma: inglés
• DOI: 10.33044/revuma.1861
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• Resumen

  • 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].