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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-05-01
|
| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2021-0041 |
| _version_ | 1819001734186401792 |
|---|---|
| author | Kaya Esra |
| author_facet | Kaya Esra |
| author_sort | Kaya Esra |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T22:53:55Z |
| format | Article |
| id | doaj.art-4748c6e8a41244f69bf3938d7df26ba5 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-20T22:53:55Z |
| publishDate | 2021-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-4748c6e8a41244f69bf3938d7df26ba52022-12-21T19:24:09ZengDe GruyterOpen Mathematics2391-54552021-05-0119130631510.1515/math-2021-0041A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spacesKaya Esra0Dumlupinar University, Department of Mathematics, Kutahya, TurkeyIn 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.https://doi.org/10.1515/math-2021-0041b-maximal operatorgeneralized translation operatorsingular integralsvariable exponent lebesgue spaces42a5042b2542b35 |
| spellingShingle | Kaya Esra A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces Open Mathematics b-maximal operator generalized translation operator singular integrals variable exponent lebesgue spaces 42a50 42b25 42b35 |
| title | A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces |
| title_full | A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces |
| title_fullStr | A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces |
| title_full_unstemmed | A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces |
| title_short | A note on maximal operators related to Laplace-Bessel differential operators on variable exponent Lebesgue spaces |
| title_sort | note on maximal operators related to laplace bessel differential operators on variable exponent lebesgue spaces |
| topic | b-maximal operator generalized translation operator singular integrals variable exponent lebesgue spaces 42a50 42b25 42b35 |
| url | https://doi.org/10.1515/math-2021-0041 |
| work_keys_str_mv | AT kayaesra anoteonmaximaloperatorsrelatedtolaplacebesseldifferentialoperatorsonvariableexponentlebesguespaces AT kayaesra noteonmaximaloperatorsrelatedtolaplacebesseldifferentialoperatorsonvariableexponentlebesguespaces |