  Let $1 \leq p < q < \infty$. We show that \[ \sup{\frac{\left\|
D\right\|_{\mathcal{H}_{q}}}{\left\| D\right\|_{\mathcal{H}_{p}}}} =
\exp{\left( \frac{\log{x}}{\log{\log{x}}} \left(\log{\sqrt{\frac{q}{p}}} +
\left(\frac{\log{\log{\log{x}}}}{\log{\log{x}}}\right)\right) \right)} \,,\]
where the supremum is taken over all non-zero Dirichlet polynomials of the form
$D(s)=\sum_{n \leq x}{a_{n} n^{-s}}$. An aplication is given to the study of
multipliers between Hardy spaces of Dirichlet series.

Complex Variables;Functional Analysis