Hardy-Littlewood inequalities and Fourier multipliers on SU(2)

Abstract

In this paper we prove a noncommutative version of Hardy-Littlewood inequalities relating a function and its Fourier coefficients on the group $SU(2)$. As a consequence, we use it to obtain lower bounds for the $L^p-L^q$ norms of Fourier multipliers on the group $SU(2)$, for $1<p\le 2\le q<1$. In addition, we give upper bounds of a similar form, analogous to the known results on the torus, but now in the noncommutative setting of $SU(2)$.

To appear in Studia Math

Cited by in corpus (2)

• Fourier multipliers and group von Neumann algebras
• Hardy-Littlewood, Hausdorff-Young-Paley inequalities, and Lp-Lq Fourier multipliers on compact homogeneous manifolds