Hardy–Littlewood–Paley inequalities and Fourier multipliers on SU(2)

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 L-p - L-q norms of Fourier multipliers on SU(2) for 1 < p <= 2 <= q < infinity. 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).