Fourier Multipliers on Quasi-Banach Orlicz Spaces and Orlicz Modulation Spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908561845518336 |
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| author | Petersson, Albin |
| author_facet | Petersson, Albin |
| contents | We find that if a Fourier multiplier is continuous from $L^{Φ_1}$ to $L^{Φ_2}$, then it is also continuous from $M^{Φ_1,Ψ}$ to $M^{Φ_2,Ψ}$, where $Φ_1,Φ_2,Ψ$ are quasi-Young functions and $Φ_1$ fulfills the $Δ_2$-condition. This result is applied to show that Mihlin's Fourier multiplier theorem and Hörmander's improvement hold in certain Orlicz modulation spaces. Lastly, we show that the Fourier multiplier with symbol $m(ξ) = e^{i μ(ξ)}$, where $μ$ is homogeneous of order $α$, is bounded on quasi-Banach Orlicz modulation spaces of order $r$, assuming $r\in\big(d/(d+2),1\big]$ and $α\in\big(d(1-r)/r, 2\big]$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12484 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fourier Multipliers on Quasi-Banach Orlicz Spaces and Orlicz Modulation Spaces Petersson, Albin Functional Analysis We find that if a Fourier multiplier is continuous from $L^{Φ_1}$ to $L^{Φ_2}$, then it is also continuous from $M^{Φ_1,Ψ}$ to $M^{Φ_2,Ψ}$, where $Φ_1,Φ_2,Ψ$ are quasi-Young functions and $Φ_1$ fulfills the $Δ_2$-condition. This result is applied to show that Mihlin's Fourier multiplier theorem and Hörmander's improvement hold in certain Orlicz modulation spaces. Lastly, we show that the Fourier multiplier with symbol $m(ξ) = e^{i μ(ξ)}$, where $μ$ is homogeneous of order $α$, is bounded on quasi-Banach Orlicz modulation spaces of order $r$, assuming $r\in\big(d/(d+2),1\big]$ and $α\in\big(d(1-r)/r, 2\big]$. |
| title | Fourier Multipliers on Quasi-Banach Orlicz Spaces and Orlicz Modulation Spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2505.12484 |