Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory
By Javier Parcet. 2007
101 citations recorded by the source corpus.
In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund operators acting over operator-valued functions. Our main tools for its solution are a noncommutative form of Calderon-Zygmund decomposition in conjunction with a pseudo-localization principle for singular integrals, which is new even in the classical setting and of independent interest. Perhaps because of the hidden role of pseudo-localization and almost orthogonality, this problem has remained open for quite some time. We also consider Calderon-Zygmund operators associated to certain operator-valued kernels.
View Paper: https://www.semanticscholar.org/paper/88ce49160bc4837f0f57f9e09274f07349aa4187
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- Marius Junge
- Javier Parcet
- Tao Mei
- Quanhua Xu
- A. Gonz'alez-P'erez
- Xiaolei Xiong
- Zhi Yin
- Narcisse Randrianantoanina
Citations in the corpus
- Singular integrals in quantum Euclidean spaces (2017, methodology): “Noncommutative martingale methods were used in [56] to establish endpoint estimates for singular integrals over tensor product von Neumann algebras with an Euclidean factor, which have been the key for the recent solution in [12] of the Nazarov-Peller conjecture.”
- Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori (2015, result): “The following lemma should be known to experts; it is closely related to similar results of [29, 46, 51], notably to [35, Lemma 2.”
- Pseudo-Localization of Singular Integrals and Noncommutative Littlewood–Paley Inequalities (2008, methodology): “where Rx is the only cube in Qk containing x and Qy is the only cube in Qk+s containing y. Moreover, the cubes Q2,Q3,...,Q2n represent the remaining cubes in Qk+s sharing dyadic father with Qy. Arguing as in [ 24 ], it is easily checked that the kernel ks,k(x,y) of EkT k+s has the form”
- Smooth Fourier multipliers on group von Neumann algebras (2010, background): “Note that Lp(Rj) = Lp(R;Lp(Mj)), so that this framework does not fall in the vector-valued theory because we take values in different Banach spaces for different values of p, see [54] for further explanations.”