Compact embedding derivatives of Hardy spaces into Lebesgue spaces

Abstract

We characterize the positive Borel measures such that the differentiation operator of order n ∈ N ∪ { 0 } n\in \mathbb {N}\cup \{0\} is compact from the Hardy space H p H^p into L q ( μ ) L^q(\mu ) , 0 > p , q > ∞ 0>p,q>\infty .