Radial Fourier multipliers in high dimensions

By Yaryong Heo, Fedor Nazarov, Andreas Seeger. 2009

67 citations recorded by the source corpus.

Given a fixed p≠2, we prove a simple and effective characterization of all radial multipliers of $ \mathcal{F}{L^p}\left( {{\mathbb{R}^d}} \right) $, provided that the dimension d is sufficiently large. The method also yields new Lq space-time regularity results for solutions of the wave equation in high dimensions.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f19efe92df63f91e94bbd5f8916ffdfabba5e7f2

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

In Mathematical Physics

Citations in the corpus

A sharp square function estimate for the cone in ℝ3 (2019, methodology): “Later in the work [15] of Heo, Nazarov and Seeger it was conjectured further that when p > 4 the conjecture should hold for α ≥ 1 2 − 2 p .”
Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds (2018, background): “The results of [43] were improved and extended by a number of authors [25, 15, 16, 4] before the remarkable breakthrough of Bourgain– Demeter [6] established essentially sharp decoupling estimates in all dimensions (see also [22, 28, 26] for alternative approaches to the local smoothing problem and ”
Some Problems in Harmonic Analysis (2017, background): “Inequality (7) is also known to imply an endpoint version of the so-called local smoothing conjecture (see [45] for the wave equation, and for an endpoint estimate for cone multipliers in Rd+1, see [25], [26]).”