Dyadic shifts and a logarithmic estimate for Hankel operators with matrix symbol

By S. Petermichl. 2000

164 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/490cda1ec8e34ed6e58ef2ef26973efa223f1973

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Weighted little bmo and two-weight inequalities for Journé commutators (2017, methodology): “Recently, this was extended to the n-dimensional case of Calderón-Zygmund operators in [11], using the modern dyadic methods started by [19] and continued in [12].”
Sharp weighted estimates for classical operators (2010, methodology): “Recently, Lacey, Petermichl and Reguera-Rodriguez [28] gave a proof of the sharp A2 constant for a large family of Haar shift operators that includes all of the dyadic operators needed for the above results.”
Sharp weighted norm estimates beyond Calderón–Zygmund theory (2015, unknown): “The idea of dyadic shift [Petermichl 2000] and the seminal articles on two-weight questions of dyadic operators by Nazarov, Treil and Volberg [Nazarov et al. 1999; 2008] were very inﬂuential in this area at that point.”
The sharp weighted bound for the Riesz transforms (2007, background): “In [11] the author introduced new dyadic model operators that seem better suited for antisymmetric operators.”
Commutators in the two-weight setting (2015, background): “We follow the outlines of that proof in the current setting, which has its genesis in [35].”
The sharp bound for the Hilbert transform on weighted Lebesgue spaces in terms of the classical A p characteristic (2007, methodology): “In [22] the author introduced new dyadic model operators that seem better suited for antisymmetric operators.”
Operator Valued Hardy Spaces (2003, background): “ operator valued Carleson measures, operator valued Hardy spaces.... A lot of works have been done notably by F. Nazazov, S. Treil and A. Volberg; see, for instance, the recent works [6], [17], [18], [20]). The second direction which motivates this paper is the non-commutative martingale theory. Thi”
Sharp A2 inequality for Haar shift operators (2009, methodology): “Prior proofs relied strongly on Haar shift operators [11] and Bellman function techniques.”
Why the Riesz transforms are averages of the dyadic shifts (2002, background): “Abstract The first author showed in [18] that the Hilbert transform lies in the closed convex hull of dyadic singular operators —so-called dyadic shifts.”
Weighted Norm Inequalities for Paraproducts and Bilinear Pseudodifferential Operators with Mild Regularity (2009, unknown): “3 complements the approaches in [21], [22], [31], [32] [37], [36], [40], and [46], where, in turn, classical Fourier Analysis operators are reduced or decomposed into paraproducts.”