The Cesàro space of Dirichlet series and its multiplier algebra

We consider the space $\mathcal{H}(ce{s}_p)$ of all Dirichlet series whose coefficients belong to the Cesàro sequence space $ce{s}_p$, consisting of all complex sequences whose absolute Cesàro means are in ${\mathrm{\ell }}^p$, for $1<p<\mathrm{\infty }$. It is a Banach space of analytic functions, for which we study the maximal domain of analyticity and the boundedness of point evaluations. We identify the algebra of analytic multipliers on $\mathcal{H}(ce{s}_p)$ as the Wiener algebra of Dirichlet series shifted to the vertical half-plane ${\mathbb{C}}_{1\mathrm{/}q}:=\{s\in \mathbb{C}:\mathrm{\Re }s>1\mathrm{/}q\}$, where $1\mathrm{/}p+1\mathrm{/}q=1$.