Boundedness of bilinear radial Fourier multipliers
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909990302777344 |
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| author | Honzík, Petr Maleček, Matyáš |
| author_facet | Honzík, Petr Maleček, Matyáš |
| contents | We show that a bilinear radial Fourier multiplier operator with symbol $σ$ is $L^2(\R^n)\times L^2(\R^n) \to L^1(\R^n)$ bounded, $n\in \mathbb N,$ if the function $σ$ satisfies the smoothness condition $σ(2^j\cdot)Φ\in L^2_{1/2 +ε}(\mathbb R^{2n})$ for some $ε>0$ and every $j\in \mathbb Z,$ where $Φ$ is a smooth cutoff function adapted to the annulus $|x|\in [1/4,4]$. This condition is dimension free. We also apply similar reasoning to provide alternative proof of the initial result concerning multilinear Bochner-Riesz operator and prove an estimate for generalized bilinear Bochner-Riesz operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09412 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Boundedness of bilinear radial Fourier multipliers Honzík, Petr Maleček, Matyáš Classical Analysis and ODEs 42B15 We show that a bilinear radial Fourier multiplier operator with symbol $σ$ is $L^2(\R^n)\times L^2(\R^n) \to L^1(\R^n)$ bounded, $n\in \mathbb N,$ if the function $σ$ satisfies the smoothness condition $σ(2^j\cdot)Φ\in L^2_{1/2 +ε}(\mathbb R^{2n})$ for some $ε>0$ and every $j\in \mathbb Z,$ where $Φ$ is a smooth cutoff function adapted to the annulus $|x|\in [1/4,4]$. This condition is dimension free. We also apply similar reasoning to provide alternative proof of the initial result concerning multilinear Bochner-Riesz operator and prove an estimate for generalized bilinear Bochner-Riesz operator. |
| title | Boundedness of bilinear radial Fourier multipliers |
| topic | Classical Analysis and ODEs 42B15 |
| url | https://arxiv.org/abs/2601.09412 |