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42-XX Harmonic analysis on Euclidean spaces
42Bxx Harmonic analysis in several variables
42B25 Maximal functions, Littlewood-Paley theory

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Une remarque sur les inégalités de Littlewood-Paley sous l’hypothèse $Γ_{2} \geq 0$

Dominique Bakry (1985)

Séminaire de probabilités de Strasbourg

Uniform bounds for the bilinear Hilbert transforms (II).

Xiaochun Li (2006)

Revista Matemática Iberoamericana

We continue the investigation initiated in [Grafakos, L. and Li, X.: Uniform bounds for the bilinear Hilbert transforms (I). Ann. of Math. (2)159 (2004), 889-933] of uniform Lp bounds for the family of bilinear Hilbert transformsHα,β(f,g)(x) = p.v. ∫R f(x - αt) g (x - βt) dt/t.

Uniform estimates for some paraproducts.

Li, Xiaochun (2008)

The New York Journal of Mathematics [electronic only]

Unique continuation for the solutions of the laplacian plus a drift

Alberto Ruiz, Luis Vega (1991)

Annales de l'institut Fourier

We prove unique continuation for solutions of the inequality $| Δ u (x) | \leq V (x) | \nabla u (x) |$ , $x \in Ω$ a connected set contained in $R^{n}$ and $V$ is in the Morrey spaces $F^{α, p}$ , with $p \geq (n - 2) / 2 (1 - α)$ and $α < 1$ . These spaces include $L^{q}$ for $q \geq (3 n - 2) / 2$ (see [H], [BKRS]). If $p = (n - 2) / 2 (1 - α)$ , the extra assumption of $V$ being small enough is needed.

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