Norm estimates for a broad class of modulation spaces, and continuity of Fourier type operators
2026 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 290, no 1, article id 111177Article in journal (Refereed) Published
Abstract [en]
We consider a broad class of modulation spaces M(ω, B),parameterized with weight function ω and a normal quasiBanach function space B of order r0 ∈ (0, 1]. Then we provethat f ∈ M(ω, B), if and only if Vϕf belongs to the Wieneramalgam space Wr(ω, B), and
∥f∥M(ω,B) ≍ ∥Vϕf · ω∥B ≍ ∥Vϕf∥Wr(ω,B), r ∈ [r0, ∞].
We use the results to extend and improve continuity andlifting properties for pseudo-differential and Toeplitz operatorswith symbols in weighted M∞,r0 -spaces, r0 ≤ 1, when actingon M(ω, B)-spaces.
Place, publisher, year, edition, pages
Elsevier, 2026. Vol. 290, no 1, article id 111177
Keywords [en]
time-frequency analysis, modulation spaces, wiener amalgam spaces, quasi-banach spaces, pseudo-differential operators, toeplitz operators
National Category
Mathematical Analysis
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-141794DOI: 10.1016/j.jfa.2025.111177ISI: 001572450900001Scopus ID: 2-s2.0-105015468145OAI: oai:DiVA.org:lnu-141794DiVA, id: diva2:2002066
2025-09-292025-09-292026-07-06Bibliographically approved