Hardy--Littlewood inequalities for the Heckman--Opdam transform

Abstract

We establish Hardy--Littlewood inequalities for the Heckman--Opdam transform associated to a general root datum $(\mathfrak{a},\Sigma ,m)$ that generalizes an analogous result for the spherical Fourier transform on a Riemannian symmetric space of the non-compact type due to Eguchi and Kumahara. In particular we obtain a more precise Hausdorff--Young inequality that generalizes a recent result due to Narayanan, Pasquale, and Pusti.

References in corpus (1)

• Paley-Wiener theorems for the Dunkl transform

Cited by in corpus (1)

• Weighted inequalities and uncertainty principles for the $(\mathbf{k},\mathbf{a})$-generalized Fourier transform