In this paper, we obtain the sharp conditions of the inclusion relationsbetween modulation spaces $M_{p,q}^s$ and Triebel-Lizorkin spaces $F_{p,r}$ for$p\leq 1$, which greatly improve and extend the results for the embeddingrelations between local Hardy spaces and modulation spaces obtained byKobayashi, Miyachi and Tomita in [Studia Math. 192 (2009), 79-96].
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机译：在本文中，我们获得了调制空间$ M_ {p，q} ^ s $与Triebel-Lizorkin空间$ F_ {p，r} $ for $ p \ leq 1 $之间的包含关系的尖锐条件，这极大地改善了扩展了由Kobayashi，Miyachi和Tomita在[Studia Math。 192（2009），79-96]。
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