ENDPOINT MAPPING PROPERTIES OF SPHERICAL MAXIMAL OPERATORS

By Andreas Seeger, Terence Tao, James Wright. Journal of the Institute of Mathematics of Jussieu, 2002

50 citations recorded by the source corpus.

For a function $f\in L^p(\mathbb{R}d)$, $d\ge 2$, let $A_tf(x)$ be the mean of $f$ over the sphere of radius $t$ centred at $x$. Given a set $E\subset(0,\infty)$ of dilations we prove various endpoint bounds for the maximal operator $M_E$ defined by $M_E f(x)=\sup_{t\in E}|A_tf(x)|$, under some regularity assumptions on $E$. AMS 2000 Mathematics subject classification: Primary 42B25. Secondary 42B20

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/fd554b21d12b2679d9453eac8b4b9abd1a23ea5a

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. Andreas Seeger
2. Eunhee Jeong
3. James Wright
4. Roger L. Jones
5. Sanghyuk Lee
6. Larry Guth
7. Keith McKenzie Rogers
8. Mariusz Mirek

In Geometry and Topology

1. Roger L. Jones
2. Andreas Seeger
3. James Wright
4. Sanghyuk Lee
5. Eunhee Jeong

Citations in the corpus

• Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators (2019, background): “‖f‖ L d d−1 ,1 when d ≥ 3 but failure of such estimate when d = 2 was shown by Seeger, Tao, and Wright [44].”
• Strong variational and jump inequalities in harmonic analysis (2008, methodology): “To show (57) we only need to check the estimate on atoms; we use arguments from [45] (see also [17], [ 43 ]).”