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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2601.15815 |
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| _version_ | 1866917476188553216 |
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| author | Carro, María Jesús Salguero-Alarcón, Alberto |
| author_facet | Carro, María Jesús Salguero-Alarcón, Alberto |
| contents | The paper focuses on the behaviour of unimodular Fourier multipliers with exponential growth in the context of weighted $L^p$-spaces. Our main result shows that much of the general theory of multipliers is approachable through the theory of unimodular multipliers. Indeed, we show that a bounded measurable function $m$ is a multiplier on $L^p$ for $1\leq p<\infty$ provided that $e^{itm}$ is a multiplier on $L^p$ and its multiplier norm admits an exponential bound of the form $e^{c|t|^s}$ for suitable $c>0$ and $0<s<1$. We then apply this principle to obtain new results related to the boundedness of homogeneous rough operators, singular operators along curves and oscillatory integrals. A key ingredient in our study is an extension of the classical Stein's theorem on analytic families of operators that studies the behaviour of the derivative operator when $θ\to 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15815 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New results on Fourier multipliers on $L^p$: a perspective through unimodular symbols Carro, María Jesús Salguero-Alarcón, Alberto Functional Analysis Primary:42B15, secondary: 42B20, 46M35 The paper focuses on the behaviour of unimodular Fourier multipliers with exponential growth in the context of weighted $L^p$-spaces. Our main result shows that much of the general theory of multipliers is approachable through the theory of unimodular multipliers. Indeed, we show that a bounded measurable function $m$ is a multiplier on $L^p$ for $1\leq p<\infty$ provided that $e^{itm}$ is a multiplier on $L^p$ and its multiplier norm admits an exponential bound of the form $e^{c|t|^s}$ for suitable $c>0$ and $0<s<1$. We then apply this principle to obtain new results related to the boundedness of homogeneous rough operators, singular operators along curves and oscillatory integrals. A key ingredient in our study is an extension of the classical Stein's theorem on analytic families of operators that studies the behaviour of the derivative operator when $θ\to 0$. |
| title | New results on Fourier multipliers on $L^p$: a perspective through unimodular symbols |
| topic | Functional Analysis Primary:42B15, secondary: 42B20, 46M35 |
| url | https://arxiv.org/abs/2601.15815 |