The Cesàro space of Dirichlet series and its multiplier algebra

Abstract

We consider the space H(cesp) of all Dirichlet series whose coefficients belong to the Cesàro sequence space cesp, consisting of all complex sequences whose absolute Cesàro means are in ℓp, for 1<p<∞. 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 H(cesp) as the Wiener algebra of Dirichlet series shifted to the vertical half-plane C1/q:={s∈C:ℜs>1/q}, where 1/p+1/q=1.