Maximal operators given by Fourier multipliers with dilation of fractional dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915590241779712 |
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| author | Lee, Jin Bong Seo, Jinsol |
| author_facet | Lee, Jin Bong Seo, Jinsol |
| contents | In this paper, we investigate $L^p$ bounds of maximal Fourier multiplier operators with dilation of fractional dimensions. For Fourier multipliers, we suggest a criterion related to dimensions of dilation sets which guarantees $L^p$ bounds of the maximal operators for each $p$. Our criterion covers Mikhlin-type multipliers, multipliers with limited decay, and multipliers with slow decay. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal operators given by Fourier multipliers with dilation of fractional dimensions Lee, Jin Bong Seo, Jinsol Classical Analysis and ODEs 42B25, 42B15, 42B35, 42B37 In this paper, we investigate $L^p$ bounds of maximal Fourier multiplier operators with dilation of fractional dimensions. For Fourier multipliers, we suggest a criterion related to dimensions of dilation sets which guarantees $L^p$ bounds of the maximal operators for each $p$. Our criterion covers Mikhlin-type multipliers, multipliers with limited decay, and multipliers with slow decay. |
| title | Maximal operators given by Fourier multipliers with dilation of fractional dimensions |
| topic | Classical Analysis and ODEs 42B25, 42B15, 42B35, 42B37 |
| url | https://arxiv.org/abs/2405.16855 |