  In this paper, we establish the sharp conditions for the inclusion relations
between Besov spaces $B_{p,q}$ and Wiener amalgam spaces $W_{p,q}^s$. We also
obtain the optimal inclusion relations between local hardy spaces $h^p$ and
Wiener amalgam spaces $W_{p,q}^s$, which completely improve and extend the main
results obtained by Cunanana, Kobayashib and Sugimotoa in [J. Funct. Anal. 268
(2015), 239-254]. In addition, we establish some mild characterizations of
inclusion relations between Triebel-Lizorkin and Wiener amalgam spaces, which
relates some modern inequalities to classical inequalities.

Classical Analysis and ODEs