Schatten class property of commutators of singular integrals on twisted crossed products

Quanhua Xu (University of Franche-Comté)

Thursday 22nd February 16:00-17:00 Maths 116


Given a twisted W*-dynamic system $(\M, \a, \s, \real^d)$ we consider the associated twisted crossed product $\M\rtimes_{\a, \s}\real^d$. Let $\phi: \real^d\setminus \{0\}\to\com$ be a $C^\infty$ function homogeneous of degree zero. The associated Fourier multiplier is a bounded operator on $L_2(\M\rtimes_{\a, \s}\real^d)$. For $x\in\M\rtimes_{\a, \s}\real^d$ the commutator $\mathbf{C}_{\phi, x}=   [T_\phi,\,   M_x]$ is then a bounded operator on $L_2(\M\rtimes_{\a, \s}\real^d)$, where $M_x$ is the left multiplication by $x$. We Characterize the membership of $\mathbf{C}_{\phi, x}$ in the Schatten $p$-class $S_p(L_2(\M\rtimes_{\a, \s}\real^d))$ by the membership of the symbol $x$ in a certain Besov space.

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