Almost everywhere convergence of Bochner-Riesz means on some Sobolev type spaces

TL;DR

This paper studies the almost everywhere convergence of Bochner-Riesz means on various Sobolev spaces, establishing the relationship between function smoothness and convergence rates.

Contribution

It extends the understanding of Bochner-Riesz means convergence to Sobolev spaces with different smoothness levels, including new results for $H^q$-Sobolev spaces.

Findings

Convergence rates depend on the smoothness of functions.

Results apply to $L^p$-Sobolev and $H^q$-Sobolev spaces.

Provides conditions for almost everywhere convergence.

Abstract

In this paper, we investigate the convergence of the Bochner-Riesz means on some Sobolev type spaces including $L^p$-Sobolev spaces $(p\geq 1)$ and $H^q$-Sobolev spaces $(0<q<1)$. The relation between the smoothness imposed on functions and the rate of almost everywhere convergence of the generalized Bochner-Riesz means is given.