Fractional medians and their maximal functions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909267322208256 |
|---|---|
| author | Tsutsui, Yohei |
| author_facet | Tsutsui, Yohei |
| contents | In this article, we introduce the fractional medians, give an expression of the set of all fractional medians in terms of non-increasing rearrangements and then investigate mapping properties of the fractional maximal operators defined by such medians. The maximal operator is a generalization of that in Stromberg. It turns out that our maximal operator is a more smooth operator than the usual fractional maximal operator. Further, we give another proof of the embedding from $BV$ to $L^{n/(n-1),1}$ due to Alvino by using the usual medians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional medians and their maximal functions Tsutsui, Yohei Classical Analysis and ODEs 42B02, 46E30, 46E35 In this article, we introduce the fractional medians, give an expression of the set of all fractional medians in terms of non-increasing rearrangements and then investigate mapping properties of the fractional maximal operators defined by such medians. The maximal operator is a generalization of that in Stromberg. It turns out that our maximal operator is a more smooth operator than the usual fractional maximal operator. Further, we give another proof of the embedding from $BV$ to $L^{n/(n-1),1}$ due to Alvino by using the usual medians. |
| title | Fractional medians and their maximal functions |
| topic | Classical Analysis and ODEs 42B02, 46E30, 46E35 |
| url | https://arxiv.org/abs/2407.17700 |