Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916351980863488 |
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| author | Cen, Xi |
| author_facet | Cen, Xi |
| contents | Let $(X,d,μ)$ is a space of homogeneous type, we establish a new class of fractional-type variable weights $A_{p(\cdot), q(\cdot)}(X)$. Then, we get the new weighted strong-type and weak-type characterizations for fractional maximal operators $M_η$ on weighted variable Lebesgue spaces over $(X,d,μ)$. This study generalizes the results by Cruz-Uribe-Fiorenza-Neugebauer (2012), Bernardis-Dalmasso-Pradolini (2014), Cruz-Uribe-Shukla (2018), and Cruz-Uribe-Cummings (2022). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15550 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type Cen, Xi Classical Analysis and ODEs Functional Analysis 42B25, 42B35 Let $(X,d,μ)$ is a space of homogeneous type, we establish a new class of fractional-type variable weights $A_{p(\cdot), q(\cdot)}(X)$. Then, we get the new weighted strong-type and weak-type characterizations for fractional maximal operators $M_η$ on weighted variable Lebesgue spaces over $(X,d,μ)$. This study generalizes the results by Cruz-Uribe-Fiorenza-Neugebauer (2012), Bernardis-Dalmasso-Pradolini (2014), Cruz-Uribe-Shukla (2018), and Cruz-Uribe-Cummings (2022). |
| title | Fractional maximal operators on weighted variable Lebesgue spaces over the spaces of homogeneous type |
| topic | Classical Analysis and ODEs Functional Analysis 42B25, 42B35 |
| url | https://arxiv.org/abs/2404.15550 |