Interpolation between non-commutative BMO and non-commutative Lp-spaces

By Magdalena Musat. 2003

67 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c74896f7f9d9a728cb700bcb95d990c4b5670e38

How researchers see this paper

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

In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Operator Valued Hardy Spaces (2003, methodology): “rojection pof M with τ(p) <∞,denote by Hq,D c (L∞(−2k,2k) ⊗ pMp) the subspace of Hq,D c (L∞(R) ⊗ M) consisting of elements supported on (−2k,2k) and with values in pMp. By dualizing Theorem 3.1 of [22] we get, for 1 <r≤ q<∞, H1,D c (L ∞(−2k,2k) ⊗pMp),H r r−1 ,D c (L∞(−2k,2k) ⊗pMp) r q = H”
BMO spaces associated with semigroups of operators (2011, background): “l work on martingales in The 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 functi”
Conditioned square functions for noncommutative martingales (2005, background): “in this subject have appeared in the literatures. These include a non-commutative analogue of Doob’s maximal functions obtained by Junge in [23], non-commutative martingale BMO-spaces were studied in [38, 34] and the analogue of the classical John-Nirenberg inequalities were recently proved in [24].”
Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory (2007, background): “Although this approach might look much simpler, the proof of the necessary interpolation results from [41] and of the noncommutative John-Nirenberg theorem (used in Mei’s argument) are also quite technical.”
Pseudo-Localization of Singular Integrals and Noncommutative Littlewood–Paley Inequalities (2008, methodology): “Given a function f in L2 and any integer k, we † Musat’s constants were improved to ∼ p for p > 2 after Randrianantoanina’s work [30]. define Ωk to be the smallest Rk-set containing the support of dfk+s.”
A Weak Type Inequality for Non‐Commutative Martingales and Applications (2004, background): “We note also a very recent result of Musat [32] on interpolation involving non-commutative BMO and non-commutative L-spaces as endpoints.”
On the Best Constants in Some Non‐Commutative Martingale Inequalities (2005, methodology): “It was proved in [9] (using tools from [13]) that βp remains bounded as p → 1, as expected due to the fact that the second inequality in (1) remains true for p = 1 (see [16, 17]).”
Gundy's Decomposition for Non‐Commutative Martingales and Applications (2004, background): “Martingale BMO spaces were studied in [24, 22, 16] and some weak type inequalities can be found in [27, 28].”