Monomial convergence for holomorphic functions on ℓ_r

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Let F be either the set of all bounded holomorphic functions or the set of all m-homogeneous polynomials on the unit ball of ℓ_r. We give a systematic study of the sets of all u∈ℓ_r for which the monomial expansion ∑_α∂αf(0)/α!uα of every f converges. Inspired by recent results from the general theory of Dirichlet series, we establish as our main tool, independently interesting, upper estimates for the unconditional basis constants of spaces of polynomials on ℓ_r spanned by finite sets of monomials.