Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917738951213056 |
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| author | Bonino, Matteo Coriasco, Sandro Petersson, Albin Toft, Joachim |
| author_facet | Bonino, Matteo Coriasco, Sandro Petersson, Albin Toft, Joachim |
| contents | We deduce continuity and (global) wave-front properties of classes of Fourier multipliers, pseudo-differential, and Fourier integral operators when acting on Orlicz spaces, or more generally, on Orlicz-Sobolev type spaces. In particular, we extend H{ö}rmander's improvement of Mihlin's Fourier multiplier theorem to the framework of Orlicz spaces. We also show how Young functions $Φ$ of the Orlicz spaces are linked to properties of certain Lebesgue exponents $p_Φ$ and $q_Φ$ emerged from $Φ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_15229 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents Bonino, Matteo Coriasco, Sandro Petersson, Albin Toft, Joachim Functional Analysis We deduce continuity and (global) wave-front properties of classes of Fourier multipliers, pseudo-differential, and Fourier integral operators when acting on Orlicz spaces, or more generally, on Orlicz-Sobolev type spaces. In particular, we extend H{ö}rmander's improvement of Mihlin's Fourier multiplier theorem to the framework of Orlicz spaces. We also show how Young functions $Φ$ of the Orlicz spaces are linked to properties of certain Lebesgue exponents $p_Φ$ and $q_Φ$ emerged from $Φ$. |
| title | Fourier type operators on Orlicz spaces and the role of Orlicz Lebesgue exponents |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2309.15229 |