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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.04757 |
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| _version_ | 1866917124904058880 |
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| author | Berra, Fabio Carena, Marilina Pradolini, Gladis |
| author_facet | Berra, Fabio Carena, Marilina Pradolini, Gladis |
| contents | We give a characterization of the continuity properties of a Luxemburg maximal type operator associated to a critical radius function $ρ$ between Orlicz spaces. This goal is achieved by means of a Dini type condition that includes certain Young functions related to the maximal operator and the spaces involved. Our results provide not only weak Fefferman-Stein type inequalities but also a weak weighted estimate of modular type for the considered operators, which is interesting in its own right. On the other hand, we prove the boundedness of the Hardy-Littlewood maximal function associated to $ρ$ between Zygmund spaces of $L\,\log\,L$ type with $A_p$ weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of the continuity properties of maximal operators associated to critical radius functions via Dini type conditions Berra, Fabio Carena, Marilina Pradolini, Gladis Classical Analysis and ODEs We give a characterization of the continuity properties of a Luxemburg maximal type operator associated to a critical radius function $ρ$ between Orlicz spaces. This goal is achieved by means of a Dini type condition that includes certain Young functions related to the maximal operator and the spaces involved. Our results provide not only weak Fefferman-Stein type inequalities but also a weak weighted estimate of modular type for the considered operators, which is interesting in its own right. On the other hand, we prove the boundedness of the Hardy-Littlewood maximal function associated to $ρ$ between Zygmund spaces of $L\,\log\,L$ type with $A_p$ weights. |
| title | Characterization of the continuity properties of maximal operators associated to critical radius functions via Dini type conditions |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2512.04757 |