科研之友
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摘要
First, we consider some fundamental properties including dual spaces, complex interpolations of alpha-modulation spaces M-p,q(s,alpha) with 0 < p, q <= infinity. 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. In a subsequent paper, we will give some applications of alpha-modulation spaces to nonlinear dispersive wave equations.
