Author:
Fiorenza Alberto,Formica Maria Rosaria
Abstract
AbstractWe prove that if $$1<p<\infty $$
1
<
p
<
∞
and $$\delta :]0,p-1]\rightarrow ]0,\infty [$$
δ
:
]
0
,
p
-
1
]
→
]
0
,
∞
[
is continuous, nondecreasing, and satisfies the $$\Delta _2$$
Δ
2
condition near the origin, then This result permits to clarify the assumptions on the increasing function against the Lebesgue norm in the definition of generalized grand Lebesgue spaces and to sharpen and simplify the statements of some known results concerning these spaces.
Funder
Università Parthenope di Napoli
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
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