Variation bounds for spherical averages

TL;DR

This paper investigates the bounds of variation operators associated with spherical means, focusing on their behavior across different L^p to L^q spaces, to understand their stability and convergence properties.

Contribution

It provides new bounds for r-variation operators of spherical means, enhancing understanding of their L^p to L^q estimates and convergence behavior.

Findings

Established bounds for r-variation operators of spherical means.

Analyzed L^p to L^q estimates for these operators.

Enhanced understanding of convergence and stability of spherical averages.

Abstract

We consider $r$-variation operators for the family of spherical means, with special emphasis on $L^p\to L^q$ estimates.