Derivatives of 𝐻^{𝑝} functions

Abstract

We prove that if { z n } \{ {z_n}\} is uniformly separated and f ∈ H p f \in {H^p} , then { f ( k ) ( z n ) ( 1 − | z n | 2 ) k + 1 / p } n = 1 ∞ ∈ l p for  k = 1 , 2 , … \{ {f^{(k)}}({z_n}){(1 - {\left | {{z_n}} \right |^2})^{k + 1/p}}\} _{n = 1}^\infty \in {l^p}\;{\text {for }}k = 1,2, \ldots .