Optimal local embeddings of Besov spaces involving only slowly varying smoothness

Abstract

The aim of the paper is to establish (local) optimal embeddings of Besov spaces B-p,r(0,b) involving only a slowly varying smoothness b. In general, our target spaces are outside of the scale of Lorentz-Karamata spaces.

In particular, we improve results from Caetano et al. (2011), where the targets are (local) Lorentz-Karamata spaces. To derive such results, we apply limiting real interpolation techniques and weighted Hardy-type inequalities. (C) 2020 Elsevier Inc.

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Keywords

• Besov spaces involving only a slowly varying smoothness
• Sharp and optimal embeddings
• Limiting real interpolation
• Weighted inequalities