Sharp estimates in vector Carleson imbedding theorem and for vector paraproducts

By Fedor Nazarov, Gilles Pisier, Sergei Treil, Alexander Volberg. 2002

76 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7dc86eb64b2cd7bc4ba1b3812791337f5bb416a1

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory (2007, background): “d with good kernels, we deduce that Theorem A does not hold for T1 and T2. This is a consequence of the matrix units we have included in the kernels of our operators. Remark 6.1. We refer to [37] and [43] for a study of paraproducts associated to operator-valued kernels. There it is shown that certa”
BMO spaces associated with semigroups of operators (2011, background): “ ﬁrst author is partially supported by the NSF DMS -090145705. The second author is partially supported by NSF DMS-0901009. 1 2 M. JUNGE AND T. MEI [PX97], [JX03], [JM07], [Mus03] and [Pop00], and to [NPTV02], [Mei07] and [BP] for work on operator- or matrix-valued functions. In [Mei08] a ﬁrst appro”
On the Best Constants in Some Non‐Commutative Martingale Inequalities (2005, methodology): “Volberg [ NPTV ] for applications of the order of the UMD-constant for Schatten classes.”
Commutators in the two-weight setting (2015, background): “Several lines of investigation came out of this work: generalizations to spaces of homogeneous type, [41], multi-parameter extensions, [8,10,23,26], connections to factorization of function spaces, [1,4,6,13], div-curl lemmas, [5,22] and additional interpretations in operator theory [32, 34, 42].”
A Weak Type Inequality for Non‐Commutative Martingales and Applications (2004, background): “RANDRIANANTOANINA algebra theory, operator space theory, and matrix valued harmonic analysis which includes among other things, operator valued Carleson measures, operator valued Hardy spaces, and operator valued Hankel operators (see for instance [20, 33]).”
Smooth Fourier multipliers on group von Neumann algebras (2010, background): “plying a deeper Caldero´n-Zygmund machinery. Noncommutative Caldero´n-Zygmund theory is a brand-new ﬁeld, only preceded byrelatedworkofLust-Piquardand the authors[39, 50, 62] and indirectlyrelated to [11,32, 38, 51,53, 59, 64,78]. A majordiﬃcultyis the lack of geometric tools derived from the relati”
Operator Valued Hardy Spaces (2003, background): “nequalities, 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”
A T1 theorem for integral transformations with operator-valued kernel (2006, background): “) A similar result is also proved in [22], with the sharp dimensional estimate as in the dyadic case, for the harmonic Carleson embedding theorem; however, this is no longer in a direct correspondence to the boundedness of paraproducts as it was in the dyadic case.”