Analysis & PDE

  • Anal. PDE
  • Volume 11, Number 6 (2018), 1535-1586.

Square function estimates for the Bochner–Riesz means

Sanghyuk Lee

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Abstract

We consider the square-function (known as Stein’s square function) estimate associated with the Bochner–Riesz means. The previously known range of the sharp estimate is improved. Our results are based on vector-valued extensions of Bennett, Carbery and Tao’s multilinear (adjoint) restriction estimate and an adaptation of an induction argument due to Bourgain and Guth. Unlike the previous work by Bourgain and Guth on L p boundedness of the Bochner–Riesz means in which oscillatory operators associated to the kernel were studied, we take more direct approach by working on the Fourier transform side. This enables us to obtain the correct order of smoothing, which is essential for obtaining the sharp estimates for the square functions.

Article information

Source
Anal. PDE, Volume 11, Number 6 (2018), 1535-1586.

Dates
Received: 4 October 2017
Accepted: 12 January 2018
First available in Project Euclid: 23 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.apde/1527040819

Digital Object Identifier
doi:10.2140/apde.2018.11.1535

Mathematical Reviews number (MathSciNet)
MR3803718

Zentralblatt MATH identifier
06881250

Subjects
Primary: 42B15: Multipliers
Secondary: 35B65: Smoothness and regularity of solutions

Keywords
square function Bochner–Riesz means

Citation

Lee, Sanghyuk. Square function estimates for the Bochner–Riesz means. Anal. PDE 11 (2018), no. 6, 1535--1586. doi:10.2140/apde.2018.11.1535. https://projecteuclid.org/euclid.apde/1527040819


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