Sharp embedding relations between local Hardy and \(\alpha\)-modulation spaces (Q2043709)

An \(\alpha\)-modulation space is a generalization of a modulation space and it links modulation spaces and Besov spaces by the parameter \(\alpha\). But \(\alpha\)-modulation spaces can not be obtained by interpolation between modulation spaces and Besov spaces. In this paper the authors give optimal embedding relation between \(\alpha\)-modulation spaces and local Hardy spaces (or Sobolev spaces).