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Fourier multipliers on quasi-Banach Orlicz spaces and Orlicz modulation spaces
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-1249-2909
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We find that if a Fourier multiplier is continuous from LΦ1 to LΦ2, then it is also continuous from M Φ1,Ψ to M Φ2,Ψ, where Φ1, Φ2, Ψ are quasi-Young functions and Φ1 fulfills the ∆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) = eiµ(ξ), where µ is homogeneous of order α, is bounded on quasi-Banach Orlicz modulation spaces of order r, assuming r ∈(d/(d + 2), 1] and α ∈(d(1 − r)/r, 2].

National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:lnu:diva-141439DOI: 10.48550/arXiv.2505.12484OAI: oai:DiVA.org:lnu-141439DiVA, id: diva2:1995620
Available from: 2025-09-05 Created: 2025-09-05 Last updated: 2026-06-23
In thesis
1. Pseudo-Differential Operators, Gelfand–Shilov Spaces, and Orlicz Type Spaces
Open this publication in new window or tab >>Pseudo-Differential Operators, Gelfand–Shilov Spaces, and Orlicz Type Spaces
2025 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Växjö: Linnaeus University Press, 2025. p. 204
Series
Linnaeus University Dissertations ; 583/2025
Keywords
Gelfand-Shilov spaces, Fourier multipliers, modulation spaces, Orlicz spaces, pseudo-differential operators, Schatten-von Neumann classes, quasi-Banach spaces
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:lnu:diva-141441 (URN)10.15626/LUD.583.2025 (DOI)978-91-8082-345-6 (ISBN)978-91-8082-344-9 (ISBN)
Public defence
2025-10-01, Weber, Hus K, Växjö, 09:15 (English)
Opponent
Supervisors
Available from: 2025-09-07 Created: 2025-09-05 Last updated: 2025-11-03Bibliographically approved

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Petersson, Albin

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CiteExportLink to record
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  • apa
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