In this paper, we consider the embedding relations between any two α-modulation spaces. Based on an observation that the α-modulation space with smaller α can be regarded as a corresponding α-modulation space with larger α, we give a complete characterization of the Fourier multipliers between α-modulation spaces with different α. Then we establish a full version of optimal embedding relations between α-modulation spaces.2000 Mathematics Subject Classification. 42B35.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.