Abstract
In this note we prove the anisotropic version of the Shannon inequality. This can be conveniently realised in the setting of Folland and Stein's homogeneous groups. We give two proofs: one giving the best constant, and another one using the Kubo-Ogawa-Suguro inequality.
Funding Statement
The authors are supported by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021). Marianna Chatzakou is a postdoctoral fellow of the Research Foundation - Flanders (FWO) under the postdoctoral grant No 12B1223N. Michael Ruzhansky and Aidyn Kassymov are also supported by EPSRC grant EP/R003025/2 and the MESRK grant AP19676031, respectively.
Citation
Marianna Chatzakou. Aidyn Kassymov. Michael Ruzhansky. "Anisotropic Shannon inequality." Osaka J. Math. 61 (1) 79 - 89, January 2024.
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