Embedding and compact embedding between Bergman and Hardy spaces

Release time:2025-04-11

Journal:arXiv:2502.08406

Abstract:For Hardy spaces and weighted Bergman spaces on the open unit ball in Cn, we determine exactly when Apα⊂Hq or Hp⊂Aqα, where 0<q<∞, 0<p<∞, and −∞<α<∞. 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.

Co-author:Guanlong Bao, Pan Ma, Fugang Yan, Kehe Zhu

Indexed by:Journal paper

Discipline:Natural Science

First-Level Discipline:Mathematics

Document Type:J

Translation or Not:no