Abstract:We investigate Fourier multipliers associated with the Strichartz Fourier transform on the Heisenberg group. In particular, we establish Hörmander-type $L^{p}-L^{q}$ boundedness results for the range $1<p\leq 2\leq q<\infty$. The analysis is based on deriving suitable analogues of the Hausdorff-Young and Paley inequalities for the Strichartz Fourier transform, followed by interpolation arguments to obtain the desired multiplier estimates. As an application, we study the local well-posedness of certain nonlinear partial differential equations. Furthermore, we establish an $L^{p}$-boundedness theorem for Fourier multipliers associated with the Strichartz Fourier transform for the full range $1<p<\infty$.
| Subjects: | Functional Analysis (math.FA) |
| MSC classes: | Primary 43A85, 43A22, Secondary 42C05, 33C45 |
| Cite as: | arXiv:2605.24574 [math.FA] |
| (or arXiv:2605.24574v1 [math.FA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24574 arXiv-issued DOI via DataCite (pending registration) |
From: Prerna Gulia [view email]
[v1]
Sat, 23 May 2026 13:29:29 UTC (26 KB)
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