Complex Interpolation and the Monotonicity in the Spatial Integrability Parameter of Exponentially Weighted Modulation Spaces

Abstract

We introduce the notion of common retraction and coretraction for families of Banach spaces, formulate a framework for identifying interpolation spaces, and apply it to modulation spaces with exponential weights $E_{p,q}^s$. By constructing the domain of the common coretraction, we are able to prove $E_{o,q}^s\hookrightarrow E_{p,q}^s$ for $o\le p$, i.e. the monotonicity in the spatial integrability parameter.

16 pages