Continuous embedding between P-de Branges spaces

Abstract

Abstract In this paper we study the continuity of the embedding operator ℓ : ℋ p (E) ↪ ℋ q (E) when 0 < p < q ⩽ ∞. The necessary and sufficient condition has already been described in [10] if p > 1. In this work, we address the problem when p = 1, using a new approach, but asking some additional hypothesis about the Hermite-Biehler function E. We give also a different proof for the case p > 1.