$\mathbf{L}^p$-boundedness of the Bochner-Riesz operator

Zipeng Wang

$\mathbf{L}^p$-boundedness of the Bochner-Riesz operator

Classical Analysis and ODEs 2025-12-29 v5

Authors: Zipeng Wang

Abstract

In this paper, we give a new approach to the Bochner-Riesz summability. As a result, we show that the Bochner-Riesz operator $\mathbf{S}^\delta, 0<\Re\delta<{1\over 2}$ is bounded on $\mathbf{L}^p(\mathbb{R}^n)$ for ${n-1\over 2n}\leq {1\over p}\leq{n+1\over 2n}$ .

Keywords

Bochner-Riesz operator $L^p$-boundedness summability Fourier analysis

Cite

@article{arxiv.2501.12742,
  title  = {$\mathbf{L}^p$-boundedness of the Bochner-Riesz operator},
  author = {Zipeng Wang},
  journal= {arXiv preprint arXiv:2501.12742},
  year   = {2025}
}

Comments

The content from previous versions was developed to prove the L^p-boundedness of Bochner-Riesz operator. The regarding implication is added in this update

$\mathbf{L}^p$-boundedness of the Bochner-Riesz operator

Abstract

Keywords

Cite

Comments

Related papers