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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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