Norm estimates for a broad class of modulation spaces, and continuity of Fourier type operators
Year: 2025
Type: article
Abstract: Let $\mathscr B$ be a normal quasi-Banach function space with respect to $r_0 \in (0,1]$ and $v_0$, $ω$ be $v$-moderate, and let $r\in [r_0,\infty ]$. Then we prove that $f$ belongs to the modulation space $M(ω,\mathscr B )$, iff $V_ϕf$ belongs to the Wiener amalgam space $W ^r(ω,\mathscr B )$, and $$ \| f \| _{M(ω, \mathscr B)} \asymp \| V _ϕf \, ω\| _{\mathscr B} \asymp \| V _ϕf\| _{W ^r(ω, \mathscr B)}. $$ We also use the results to deduce continuity for pseudo-differential operators with symbols in weighted $M^{\infty,r_0}$-spaces, with $r_0\le 1$, when acting on $M(ω,\mathscr B )$-spaces.
Source: Journal of Functional Analysis
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,250
OpenAlex ID: W4413815286