  The goal of this note is to show that some convolution type inequalities from
Harmonic Analysis and Information Theory, such as Young's convolution
inequality (with sharp constant), Nelson's hypercontractivity of the Hermite
semi-group or Shannon's inequality, can be reduced to a simple geometric study
of frames of $\R^2$. We shall derive directly entropic inequalities, which were
recently proved to be dual to the Brascamp-Lieb convolution type inequalities.
