Estimates for generalized wave‐type Fourier multipliers on modulation spaces and applications

Yufeng Lu

Mathematische Nachrichten, 2024, vol. 297, issue 4, 1468-1482

Abstract: We consider the boundedness of the Fourier multipliers σt(ξ)=sin(tϕ(h(ξ)))ϕ(h(ξ))$\sigma _{t}(\xi ) = \frac{\sin (t\phi (h(\xi )))}{\phi (h(\xi ))}$ on modulation spaces, where h$h$ defined on Rd${\mathbb {R}}^{d}$ is a C∞(Rd∖0)$C^{\infty }({\mathbb {R}}^{d}\setminus \left\lbrace 0\right\rbrace )$ positive homogeneous function with degree λ>0$\lambda >0$ and ϕ:R+→R+$\phi : {\mathbb {R}}^{+} \rightarrow {\mathbb {R}}^{+}$ is a smooth function satisfying some decay conditions. We prove the boundedness of this kind of Fourier multipliers and obtain its asymptotic estimates as t$t$ goes to infinity. We remote the restriction λ>1/2$\lambda >1/2$ in Deng, Ding, and Sun's result in [Nonlinear Anal. 85 (2013), 78–92], and we consider the more general form of this multiplier. As applications, we obtain the grow‐up rate of the solutions for the Cauchy problems for the generalized wave and Klein–Gordon equations, and we obtain the local well‐posedness of nonlinear wave and Klein–Gordon equations in modulation spaces.

Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202200336

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:4:p:1468-1482

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().