8,825 research outputs found
Global Citizenship: The Role of Faith Communities in the Public Space
Article given as a public lecture at Wilfrid Laurier University, Waterloo, ON, Canada 11 June 2015
Hyperplane conjecture for quotient spaces of
We give a positive solution for the hyperplane conjecture of quotient spaces
F of , where 1
. vol(B_F)^{\frac{n-1}{n}} \kl c_0 \pl p' \pl \sup_{H \p hyperplane} vol(B_F\cap H) \pl. This result is extended to Banach lattices which does not contain 's uniformly. Our main tools are tensor products and minimal volume ratio with respect to -sections
Calder\'on-Zygmund operators associated to matrix-valued kernels
Calder\'on-Zygmund operators with noncommuting kernels may fail to be
Lp-bounded for , even for kernels with good size and smoothness
properties. Matrix-valued paraproducts, Fourier multipliers on group vNa's or
noncommutative martingale transforms are frameworks where we find such
difficulties. We obtain weak type estimates for perfect dyadic CZO's and
cancellative Haar shifts associated to noncommuting kernels in terms of a
row/column decomposition of the function. Arbitrary CZO's satisfy
type estimates. In conjunction with , we get certain
row/column Lp estimates. Our approach also applies to noncommutative
paraproducts or martingale transforms with noncommuting symbols/coefficients.
Our results complement recent results of Junge, Mei, Parcet and
Randrianantoanina
Noncommutative Bennett and Rosenthal inequalities
In this paper we extend the Bernstein, Prohorov and Bennett inequalities to
the noncommutative setting. In addition we provide an improved version of the
noncommutative Rosenthal inequality, essentially due to Nagaev, Pinelis and
Pinelis, Utev for commutative random variables. We also present new best
constants in Rosenthal's inequality. Applying these results to random Fourier
projections, we recover and elaborate on fundamental results from compressed
sensing, due to Candes, Romberg and Tao.Comment: Published in at http://dx.doi.org/10.1214/12-AOP771 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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