Characterization of inclusion relations between Wiener amalgam and some classical spaces

In this paper, we establish the sharp conditions for the inclusion relations between Besov spaces Bp,q and Wiener amalgam spaces Wp,qs. We also obtain the optimal inclusion relations between local hardy spaces hp and Wiener amalgam spaces Wp,qs, which completely improve and extend the main results obtained by Cunanana, Kobayashib and Sugimotoa in [3]. 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.