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$α$-Modulation Spaces (I) (1108.0460v4)
Published 2 Aug 2011 in math.FA
Abstract: First, we consider some fundamental properties including dual spaces, complex interpolations of $\alpha$-modulation spaces $M{s,\alpha}_{p,q}$ with $0<p,q \le \infty$. Next, necessary and sufficient conditions for the scaling property and the inclusions between $\alpha_1$-modulation and $\alpha_2$-modulation spaces are obtained. Finally, we give some criteria for $\alpha$-modulation spaces constituting multiplication algebra. As a by-product, we show that there exists an $\alpha$-modulation space which is not an interpolation space between modulation and Besov spaces.