Extensions of the vector-valued Hausdorff–Young inequalities

In this paper we study the vector-valued analogues of several inequalities for the Fourier transform. In particular, we consider the inequalities of Hausdorff–Young, Hardy–Littlewood, Paley, Pitt, Bochkarev and Zygmund. The Pitt inequalities include the Hausdorff–Young and Hardy–Littlewood inequalities and state that the Fourier transform is...