Embedding and compact embedding between Bergman and Hardy spaces

Guanlong Bao; Pan Ma; Fugang Yan; Kehe Zhu

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arXiv · 2502.08406

Embedding and compact embedding between Bergman and Hardy spaces

Guanlong Bao·Pan Ma·Fugang Yan·Kehe Zhu

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Abstract

For Hardy spaces and weighted Bergman spaces on the open unit ball in ${\mathbb C}^n$, we determine exactly when $A^p_α\subset H^q$ or $H^p\subset A^q_α$, where $0<q<\infty$, $0<p<\infty$, and $-\infty<α<\infty$. For each such inclusion we also determine exactly when it is a compact embedding. Although some special cases were known before, we are able to completely cover all possible cases here. We also introduce a new notion called {\it tight fitting} and formulate a conjecture in terms of it, which places several prominent known results about contractive embeddings in the same framework.

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BibTeX RIS

Guanlong Bao, Pan Ma, Fugang Yan, Kehe Zhu. 2025-02-12. Embedding and compact embedding between Bergman and Hardy spaces. https://arxiv.org/abs/2502.08406

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