Maximal multilinear operators

By Ciprian Demeter, Terence Tao, C. Thiele. 2005

60 citations recorded by the source corpus.

We establish multilinear L P bounds for a class of maximal multilinear averages of functions of one variable, reproving and generalizing the bilinear maximal function bounds of Lacey (2000). As an application we obtain almost everywhere convergence results for these averages, and in some cases we also obtain almost everywhere convergence for their ergodic counterparts on a dynamical system.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/06f26fc1b81cbab317b604c4bac0b4b9d3d0e5a7

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In Applied Mathematics

1. I. Assani
2. Ciprian Demeter
3. C. Thiele
4. Xiaochun Li
5. Loukas Grafakos
6. Camil Muscalu
7. Victor Lie

In Discrete Mathematics and Combinatorics

1. I. Assani
2. C. Thiele
3. Ciprian Demeter

In Numerical Analysis

1. I. Assani
2. C. Thiele
3. Ciprian Demeter
4. Xiaochun Li
5. Loukas Grafakos

Citations in the corpus

• On the two dimensional Bilinear Hilbert Transform (2008, background): “trees we will denote by kFkBMO := sup R 1 |R| X T∈F:RT⊆R |RT|, where the supremum is taken over all the dyadic squares R. Define also the counting function NF := X T∈F χR T . The following result from [5] shows that in order to achieve L1 control over the counting function ofa collection oftrees (and”
• Pointwise convergence of ergodic averages along cubes (2010, methodology): “averaging processes for powers of the same transformation were afterwards obtained by C. Demeter, T. Tao and C. Thiele [ 7 ].”
• Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators (2011, unknown): “Many authors were interested in these topics ([6], [7], [5], [18], [15], [9], [19], [22], [4], [20], [25], [13] and [2]).”