Absolutely Summing Multipliers on Hp Spaces

Abstract

Let a = a n be a sequence of complex numbers. Let d a be the induced multiplier from the Hardy space H p into the sequence space l q where 1 ≤ p q ≤ ∞. We obtain complete characterization for d a to be 2-summing or 1-summing when 1 ≤ p ≤ 2 and 1 ≤ q ≤ ∞, and we give upper and lower estimates for the 2-summing and 1-summing norms in the case 2 < p ≤ ∞ and 1 ≤ q ≤ ∞.

Compact multipliers on spaces of analytic functions

“…It's worth mentioning that p-summing multipliers were studied in the context of H p spaces (see [1]) and in reference to abstract Hardy spaces (see [13]). …”

“…For a survey of the results on multipliers from Hardy spaces H p to ℓ q for various p and q we refer to [14] and the references included therein. It's worth mentioning that p-summing multipliers were studied in [1] in case of H p spaces and within the general setting of abstract Hardy spaces in [13].…”