A proof of boundedness of the Carleson operator

By Michael T. Lacey, C. Thiele. 2000

185 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4dbe1e5cc080792ba46c674fccdc58a795b87b11

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Lp theory for outer measures and two themes of Lennart Carleson united (2013, methodology): “To prove bounds on Carleson’s operator, [12] uses modified wave packets (1.”
A variation norm Carleson theorem (2009, background): “We are also motivated by the fact that variation norms are in certain situations more stable under nonlinear perturbation than supremum norms.”
On the two dimensional Bilinear Hilbert Transform (2008, background): “But the approach in the current paper is further evidence for a unified proof for bounds of the bilinear Hilbert transform and Carleson’s operator, following up on the analogy that was stressed in [12].”
The (Weak-L2) Boundedness of the Quadratic Carleson Operator (2007, methodology): “19”
On a Conjecture of E. M. Stein on the Hilbert Transform on Vector Fields (2007, methodology): “We need a set of definitions that are inspired by the approach of Lacey and Thiele [20], and are also used in Lacey and Li [15].”
OSCILLATORY INTEGRALS RELATED TO CARLESON'S THEOREM (2001, methodology): “Lacey, combining ideas of his proof with Thiele for Carleson’s theorem [ LT ], with the arguments in [St1], has obtained the desired result in the case when n =1 ,d = 2. (See [L]).”
A Carleson type theorem for a Cantor group model of the scattering transform (2002, methodology): “We propose to study the analogue of Carleson’s theorem [5] or the sharper form by Hunt [9], see also [10] for a recent proof, for scattering transforms.”
Breaking the duality in the return times theorem (2006, unknown): “Then for each x /∈ E we have ∥∥∥∥∥∥∥ ( ∑ k∈Z | ∑ s∈P |Is|=2k asφs(x, θ)|2)1/2 ∥∥∥∥∥∥∥ M2,θ(R) . σ + γ. (101)”