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- W2950685005 abstract "For $2le p<infty$ we show the lower estimates [ |A^{frac 12}x|_p kl c(p)max{pl |Gamma(x,x)^{{1/2}}|_p,pl |Gamma(x^*,x^*)^{{1/2}}|_p} ] for the Riesz transform associated to a semigroup $(T_t)$ of completely positive maps on a von Neumann algebra with negative generator $T_t=e^{-tA}$, and gradient form [ 2Gamma(x,y)lel Ax^*y+x^*Ay-A(x^*y)pl .] As additional hypothesis we assume that $Gamma^2gl 0$ and the existence of a Markov dilation for $(T_t)$. We give applications to quantum metric spaces and show the equivalence of semigroup Hardy norms and martingale Hardy norms derived from the Markov dilation. In the limiting case we obtain a viable definition of BMO spaces for general semigroups of completely positive maps which can be used as an endpoint for interpolation. For torsion free ordered groups we construct a connection between Riesz transforms and the Hilbert transform induced by the order." @default.
- W2950685005 created "2019-06-27" @default.
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- W2950685005 date "2008-01-12" @default.
- W2950685005 modified "2023-09-27" @default.
- W2950685005 title "Noncommutative Riesz transforms -- a probabilistic approach" @default.
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