Some inequalities associated with a partial differential operator

Raoudha Laffi

doi:10.56754/0719-0646.2703.681

DOI:

https://doi.org/10.56754/0719-0646.2703.681

Abstract

We study uncertainty principles for a generalized Fourier transform \(\mathcal{F}_\alpha\), associated with the pair of partial differential operators \((D, D_\alpha)\) originally introduced by Flensted-Jensen and later extended by Trimèche. This transform, is defined via the Jacobi kernel and an appropriate weighted measure. We establish an \(\mathrm{L}^p-\mathrm{L}^{q}\) version of Miyachi’s theorem, from which we deduce Cowling-Price-type results. Additionally, we establish a local uncertainty principle in the sense of Faris and provide related numerical estimates.

Keywords

Partial differential operators , generalized Fourier transform , Jacobi kernel , Miyachi theorem , Cowling-Price theorem , uncertainty principle

Mathematics Subject Classification:

42B10 , 43A32

Raoudha Laffi Department of Mathematics, Faculty of Sciences of Tunis, LR11ES11, El Manar University, Tunis, 5100, Tunisia. https://orcid.org/0000-0003-1849-3811

Pages: 681–700
Date Published: 2025-12-24
Vol. 27 No. 3 (2025)

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