Pseudo-Localization of Singular Integrals and Noncommutative Littlewood–Paley Inequalities

By Tao Mei, Javier Parcet. 2008

51 citations recorded by the source corpus.

We prove weak type inequalities for a large class of noncommutative square functions. In conjunction with BMO type estimates, interpolation and duality, we obtain the corresponding equivalences in the whole L p scale. Examples and applications include weak type (1, 1) boundedness for the noncommutative analogs of Stein's ergodic averages, Littlewood-Paley g-functions and Lusin-area integrals or optimal constants for the Littlewood-Paley inequality of noncommutative L p valued functions.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9cb4fd9daafdfab199275ce73732770bc38a5849

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

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.”
Smooth Fourier multipliers on group von Neumann algebras (2010, background): “In particular, if we let R = L∞(R)⊗̄M, we recover the main result in [46] in terms of the spaces Lp(R; l(2)rc) = { Lp(R; l2) + Lp(R; l2) if 1 ≤ p ≤ 2, Lp(R; l2) ∩ Lp(R; l2) if 2 ≤ p ≤ ∞.”
Singular integrals in quantum Euclidean spaces (2017, unknown): “ng by left/right or Schur multiplication, other BMO spaces in a new approach towards nondoubling CZ theory, Littlewood-Paley estimates, Ho¨rmander-Mihlin multipliers or directional Hilbert transforms [15, 16, 37, 42, 54]. The Caldero´n-Zygmund theory presented below is the ﬁrst form over a ‘fully no”