| Volume 7, Number 4, 2017, Pages 1637-1651 DOI：10.11948/2017100 |
| Minimizers for the embedding of Besov spaces |
| Mingjuan Chen |
| Keywords:Profile decomposition, Besov embedding, minimizer, compactness. |
| Abstract: |
| Using the profile decomposition, we will show the relatively compactness of the minimizing sequence to the critical embeddings between Besov spaces, which implies the existence of minimizer of the critical embeddings of Besov spaces $\dot{B}^{s_1}_{p_1,q_1}\hookrightarrow \dot{B}^{s_2}_{p_2,q_2}$ in $d$ dimensions with $s_1-d/p_1=s_2-d/p_2$, $s_1>s_2$ and
$1 \leq q_1 |
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