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October, 2014 $\alpha$-modulation spaces (I) scaling, embedding and algebraic properties
Jinsheng HAN, Baoxiang WANG
J. Math. Soc. Japan 66(4): 1315-1373 (October, 2014). DOI: 10.2969/jmsj/06641315


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. In a subsequent paper, we will give some applications of $\alpha$-modulation spaces to nonlinear dispersive wave equations.


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Jinsheng HAN. Baoxiang WANG. "$\alpha$-modulation spaces (I) scaling, embedding and algebraic properties." J. Math. Soc. Japan 66 (4) 1315 - 1373, October, 2014.


Published: October, 2014
First available in Project Euclid: 23 October 2014

zbMATH: 1307.35137
MathSciNet: MR3272601
Digital Object Identifier: 10.2969/jmsj/06641315

Primary: 42B35
Secondary: 35A23 , 42B37

Keywords: $\alpha$-modulation space , dual space , ‎embedding‎ , Multiplication Algebra , Scaling property

Rights: Copyright © 2014 Mathematical Society of Japan


Vol.66 • No. 4 • October, 2014
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