Hardy-littlewood-paley inequalities and fourier multipliers on SU(2)

Abstract

We prove noncommutative versions of Hardy-Littlewood and Paley inequalities relating a function and its Fourier coefficients on the group SU(2). We use it to obtain lower bounds for the Lp-Lq norms of Fourier multipliers on SU(2) for 1 < p ≤ 2 ≤ q < ∞. 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).