Embeddings of $\alpha$-modulation spaces
  We show upper and lower embeddings of $\alpha_1$-modulation spaces in $\alpha_2$-modulation spaces for $0 \leq \alpha_1 \leq \alpha_2 \leq 1$, and prove partial results on the sharpness of the embeddings. 
Joachim Toft and Patrik Wahlberg
math.FA