In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator ( B B -maximal operator) on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces. We will give a necessary condition for the boundedness of the B B -maximal operator on variable exponent Lebesgue spaces. Moreover, we will obtain that the B B -maximal operator is not bounded on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces in the case of p − = 1 {p}_{-}=1 . We will also prove the boundedness of the fractional maximal function associated with the Laplace-Bessel differential operator (fractional B B -maximal function) on L p ( ⋅ ) , γ ( R k , + n ) {L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces.

中文翻译：

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关于可变指数Lebesgue空间上与Laplace-Bessel微分算子有关的最大算子的注记

在本文中，我们考虑与L p（），γ（R k，+ n）{L} _ {p \ left（\ cdot） ，\ gamma} \ left（{{\ mathbb {R}}} _ {k，+} ^ {n}）变量指数Lebesgue空间。我们将给出可变指数Lebesgue空间上BB-极大算子的有界性的必要条件。此外，我们将获得BB-极大算子不受L p（⋅），γ（R k，+ n）{L} _ {p \ left（\ cdot），\ gamma} \ left（{{在p − = 1 {p} _ {-} = 1的情况下，\ mathbb {R}}} _ {k，+} ^ {n}）变量指数Lebesgue空间。我们还将证明与Laplace-Bessel微分算子（分数BB-最大函数）相关的分数最大函数在L p（⋅），γ（R k，+ n）{L} _ {p \ left（ \ cdot），\ gamma} \ left（{{\ mathbb {R}}} _ {k，