The classical Hausdorff-Young inequality for locally compact abelian groups states that, for 1 ≤ p ≤ 2, the L-norm of a function dominates the L-norm of its Fourier transform, where 1/p + 1/q = 1. By using the theory of non-commutative L-spaces and by reinterpreting the Fourier transform, R. Kunze (1958) [resp. M. Terp (1980)] extended this inequality to unimodular [resp. non-unimodular] groups...

Recently Foschi gave a proof of a sharp Strichartz inequality in one and two dimensions. In this note, a new representation in terms of an orthogonal projection operator is obtained for the space time norm of solutions of the free Schrödinger equation in dimension one and two. As a consequence, the sharp Strichartz inequality follows from the elementary property that orthogonal projections do n...

We prove a Bernstein type inequality for multivariate quasipolynomials and apply it to carry out the following results. (1) The evaluation of the uniform norm for a quasipolynomial on a convex body V/R by that on a measurable subset of V. (2) The estimate of the BMO-norm for a quasipolynomial in terms of its degree and exponential type. (3) The reverse Ho lder inequality with a dimensionless co...