What question did this study set out to answer?

To establish analogues of key inequalities and theorems using the Helgason-Fourier transform in Riemannian symmetric spaces.

March 29, 2026Journal of Lie theoryOpen Access

The Helgason-Fourier Transform for Symmetric Spaces II

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Formulates inequalities and theorems for Riemannian symmetric spaces, suggesting new mathematical insights.

To establish analogues of key inequalities and theorems using the Helgason-Fourier transform in Riemannian symmetric spaces.
Formulated extensions of the Hausdorff-Young and Hardy-Littlewood-Paley inequalities.
Developed a version of the Wiener Tauberian theorem applicable to symmetric spaces.
Investigated uncertainty theorems related to the Helgason-Fourier transform.
Presented new inequalities and theorems that expand classical results to symmetric spaces.
Demonstrated the validity of these formulations on Riemannian symmetric spaces of noncompact type.

Mohanty et al. (2004) studied this question.

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