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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.01450 |
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| _version_ | 1866913499074002944 |
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| author | Bokayev, Nurzhan A. Gogatishvili, Amiran Abek, Azhan N. |
| author_facet | Bokayev, Nurzhan A. Gogatishvili, Amiran Abek, Azhan N. |
| contents | In this paper, we consider the generalized fractional maximal function and use it to introduce the space of generalized fractional maximal functions and the various cones of monotone functions generated by generalized fractional maximal functions $M_Φf$. We introduced three function classes. We give equivalent descriptions of such cones when the function $Φ$ belongs to some function classes. The conditions for their mutual covering are given. Then, these cones are used to construct a criterion for embedding the space of generalized fractional maximal functions into the rearrangement invariant spaces (RIS). The optimal RIS for such embedding is also described. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01450 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cones of monotone functions generated by a generalized fractional maximal function Bokayev, Nurzhan A. Gogatishvili, Amiran Abek, Azhan N. Functional Analysis 42B25, 46E30, 47L07, 47B38 In this paper, we consider the generalized fractional maximal function and use it to introduce the space of generalized fractional maximal functions and the various cones of monotone functions generated by generalized fractional maximal functions $M_Φf$. We introduced three function classes. We give equivalent descriptions of such cones when the function $Φ$ belongs to some function classes. The conditions for their mutual covering are given. Then, these cones are used to construct a criterion for embedding the space of generalized fractional maximal functions into the rearrangement invariant spaces (RIS). The optimal RIS for such embedding is also described. |
| title | Cones of monotone functions generated by a generalized fractional maximal function |
| topic | Functional Analysis 42B25, 46E30, 47L07, 47B38 |
| url | https://arxiv.org/abs/2406.01450 |