Victor Lie

activity

20072026

most citedMaximal operators and Hilbert transforms along variable non-flat homogeneous curves

35 citations · 111 across the 20 of their papers we have counts for

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Showing 2011Show all

3 papers · 1 filter

math.CA2011★ 3 cited

On the Boundedness of the Carleson Operator near $L^{1}$

Victor Lie

Based on the tile discretization elaborated by the author in "The Polynomial Carleson Operator", we develop a Calderon-Zygmund type decomposition of the Carleson operator. As a con…

math.CA2011★ 2 cited

On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves

Victor Lie

We are proving $L^{2} (R) \times L^{2} (R) \to L^{1} (R)$ bounds for the bilinear Hilbert transform $H_{Γ}$ along curves $Γ = (t, - γ (t))$ with $γ$ being a smooth "non-flat" curve nea…

math.CA2011★ 20 cited

The Polynomial Carleson Operator

Victor Lie

We prove affirmatively the one dimensional case of a conjecture of Stein regarding the $L^{p}$ -boundedness of the Polynomial Carleson operator, for $1 < p < \infty$ . The proof is based o…

On the Boundedness of the Carleson Operator near L1

On the Boundedness of The Bilinear Hilbert Transform along "non-flat" smooth curves

The Polynomial Carleson Operator

On the Boundedness of the Carleson Operator near $L^{1}$