P-de Branges空间之间的连续嵌入

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2021-01-01 DOI:10.1515/conop-2020-0118

Carlo Bellavita

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引用次数: 0

摘要

摘要研究了当0 < p < q≤∞时，嵌入算子h: h p(E)“h q(E)”的连续性。在[10]中已经描述了其充要条件。在这项工作中，我们使用一种新的方法解决了p = 1时的问题，但提出了一些关于Hermite-Biehler函数e的额外假设。

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Continuous embedding between P-de Branges spaces

Abstract In this paper we study the continuity of the embedding operator ℓ : ℋp(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.

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