In this paper, we give a novel proof for the following equality
$\mathop {\lim }\limits_{\alpha \to {0^ + }} {\alpha ^P}{d_f}(\alpha ) = \mathop {\lim }\limits_{\alpha \to \infty } {\alpha ^P}{d_f}(\alpha ) = 0$
for f∈Lp,q(X,μ) with 0<p<∞, and 0<q<∞.We also prove that the function αp can not be improved for some sense. When q=∞, the above equality does not hold.
WU Di
,
DENG Yangkendi
,
YU Dandan
,
YAN Dunyan
. Limiting property of distribution function in Lorentz space[J]. Journal of University of Chinese Academy of Sciences, 2023
, 40(1)
: 1
-5
.
DOI: 10.7523/j.ucas.2021.0015
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