A Classification Theorem on Non-compact Embeddings between Besov Spaces

Chian Yeong Chuah; Jan Lang; Liding Yao

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arXiv · 2410.10731

A Classification Theorem on Non-compact Embeddings between Besov Spaces

Chian Yeong Chuah·Jan Lang·Liding Yao

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Abstract

We analyze the embedding properties between Besov spaces, defined on the total space $\mathbb R^n$ and on bounded domains. We give a complete classification on whether or not these embedding maps satisfy certain weak compactness characterized by the so-called strictly and finitely strictly singular condition. The result extends the recent findings on Sobolev embeddings by offering a refined description of the quality of non-compactness in the setting of Besov spaces.

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Chian Yeong Chuah, Jan Lang, Liding Yao. 2024-10-14. A Classification Theorem on Non-compact Embeddings between Besov Spaces. https://arxiv.org/abs/2410.10731

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