A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces
In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator (BB-maximal operator) on Lp(⋅),γ(Rk,+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 BB-m...
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| Format: | article |
| Language: | EN |
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De Gruyter
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/4748c6e8a41244f69bf3938d7df26ba5 |
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| Summary: | In this paper, we consider the maximal operator related to the Laplace-Bessel differential operator (BB-maximal operator) on Lp(⋅),γ(Rk,+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 BB-maximal operator on variable exponent Lebesgue spaces. Moreover, we will obtain that the BB-maximal operator is not bounded on Lp(⋅),γ(Rk,+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 BB-maximal function) on Lp(⋅),γ(Rk,+n){L}_{p\left(\cdot ),\gamma }\left({{\mathbb{R}}}_{k,+}^{n}) variable exponent Lebesgue spaces. |
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