The Multilinear Strong Maximal Function

By Loukas Grafakos, Liguang Liu, C. P'erez, Rodolfo H. Torres. 2010

58 citations recorded by the source corpus.

A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the boundedness of this multivariable operator on products of weighted Lebesgue spaces equipped with multiple weights are obtained. Results for other multi(sub)linear maximal functions associated with bases of open sets are studied too. Bilinear interpolation results between distributional estimates, such as those satisfied by the multivariable strong maximal function, are also proved.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6caca9922d3351badc81bfd095c78c9e9f6ebcdd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dachun Yang
2. Diego Maldonado
3. Liguang Liu
4. Loukas Grafakos
5. Wen Yuan
6. Yuan Zhou
7. Jun Liu
8. Yoshihiro Sawano

In Numerical Analysis

1. Loukas Grafakos
2. Dachun Yang

Citations in the corpus

• Multilinear analysis on metric spaces (2014, background): “In [46], it was proved that if (ν, w⃗) satisfies a certain power bump condition, which is defined by replacing balls with rectangles of Rn in (4.”
• Weighted estimates for the iterated commutators of multilinear maximal and fractional type operators (2011, unknown): “Many authors were interested in these topics ([5], [6], [4], [18], [15], [8], [19], [22], [3], [20], [25], [14], [1]).”
• End‐point estimates for iterated commutators of multilinear singular integrals (2010, unknown): “It is also the right one from the point of view interpolation as recently shown by Grafakos et al [4].”