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تسجيل مستخدم جديدFree Hilbert Transforms
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We study analogues of classical Hilbert transforms as fourier multipliers on free groups. We prove their complete boundedness on non commutative $L^p$ spaces associated with the free group von Neumann algebras for all $1<p<infty$. This implies that the decomposition of the free group $F_infty$ into reduced words starting with distinct free generators is completely unconditional in $L^p$. We study the case of Voiculescus amalgamated free products of von Neumann algebras as well. As by-products, we obtain a positive answer to a compactness-problem posed by Ozawa, a length independent estimate for Junge-Parcet-Xus free Rosenthal inequality, a Littlewood-Paley-Stein type inequality for geodesic paths of free groups, and a length reduction formula for $L^p$-norms of free group von Neumann algebras.
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We introduce a class of independence relations, which include free, Boolean and monotone independence, in operator valued probability. We show that this class of independence relations have a matricial extension property so that we can easily study t
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In this paper, for $1<p<infty$, we obtain the $L^p$-boundedness of the Hilbert transform $H^{gamma}$ along a variable plane curve $(t,u(x_1, x_2)gamma(t))$, where $u$ is a Lipschitz function with small Lipschitz norm, and $gamma$ is a general curve s
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In deformation-rigidity theory it is often important to know whether certain bimodules are weakly contained in the coarse bimodule. Consider a bimodule $H$ over the group algebra $mathbb{C}[Gamma]$, with $Gamma$ a discrete group. The starting point o
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