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A characterization of the Lorentz space $L(p,r)$ in terms of Orlicz type classes
Volume 62, no. 1
(2021),
pp. 117–122
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 by the Unión Matemática Argentina |
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