Sparse Bounds for Bochner-Riesz Multipliers

Abstract

The Bochner-Riesz multipliers $B_{\delta }$ on ${\mathbb{R}}^n$ are shown to satisfy a range of sparse bounds, for all $0<\delta <\frac{n-1}{2}$. The range of sparse bounds increases to the optimal range, as $\delta$ increases to the critical value, $\delta =\frac{n-1}{2}$, even assuming only partial information on the Bochner-Riesz conjecture in dimensions $n\ge 3$. In dimension $n=2$, we prove a sharp range of sparse bounds. The method of proof is based upon a `single scale' analysis, and yields the sharpest known weighted estimates for the Bochner-Riesz multipliers in the category of Muckenhoupt weights.

15 pages, 2 figures

References in corpus (3)

• A sparse domination principle for rough singular integrals
• Sparse bilinear forms for Bochner Riesz multipliers and applications
• Sparse Endpoint Estimates for Bochner-Riesz Multipliers on the Plane

Cited by in corpus (7)

• Dyadic harmonic analysis and weighted inequalities: the sparse revolution
• Multi-scale sparse domination
• Sparse Endpoint Estimates for Bochner-Riesz Multipliers on the Plane
• Quadratic sparse domination and Weighted Estimates for non-integral Square Functions
• Sparse bounds for pseudo-multipliers associated to Grushin operators, I
• Endpoint sparse domination for classes of multiplier transformations
• Bochner-Riesz means at the critical index: Weighted and sparse bounds