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...
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | article |
| Langue: | EN |
| Publié: |
De Gruyter
2021
|
| Sujets: | |
| Accès en ligne: | https://doaj.org/article/4748c6e8a41244f69bf3938d7df26ba5 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| Résumé: | 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. |
|---|