The Cesàro space of Dirichlet series and its multiplier algebra

Abstract

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 ${\ell }^p$, for $1<p<\infty$. 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 ${\mathbb{C}}_{1/q}:=\{s\in \mathbb{C}:\Re s>1/q\}$, where $1/p+1/q=1$.