Absolutely Summing Multipliers on Hp Spaces

Let a D ”an• be a sequence of complex numbers. Let da be the induced multiplier from the Hardy space Hp into the sequence space lq where 1 p; q 1.We obtain complete characterization for da to be 2-summing or 1-summing when 1 p 2 and 1 q 1, and we give upper and lower estimates for the 2-summing and 1-summing norms in the case 2 < p 1 and 1 q 1.