Density of the Derivatives of Simple Partial Fractions in Hardy Spaces in the Half-Plane. II

We prove that, for positive integers L ≥ 3 , the sums ∑ₖ₌₁ⁿ 1(z-aₖ)L, Im aₖ < 0, n ∈ N, are dense in all Hardy spaces Hₚ in the upper half-plane for 1 ≤ p< ∞ , as well as in the space of functions analytic in the upper half-plane, continuous in its closure, and tending to zero at infinity.