Optimal comparison of $P$-norms of Dirichlet Polynomials

Andreas Defant, Antonio Pérez

Let $1\le p<q<\infty$. 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…