$L^p$-boundeness properties of variation operators in the Schrodinger setting

TL;DR

This paper proves the $L^p$-boundedness of variation operators linked to heat semigroups, Riesz transforms, and their commutators with BMO functions within the Schrödinger framework.

Contribution

It establishes new $L^p$-boundedness results for variation operators in the Schrödinger setting, extending classical harmonic analysis tools.

Findings

Proves $L^p$-boundedness of variation operators for heat semigroups

Establishes boundedness for Riesz transforms and their commutators with BMO functions

Extends harmonic analysis results to Schrödinger operators

Abstract

In this paper we establish the $L^p$-boundedness properties of the variation operators associated with the heat semigroup, Riesz transforms and commutator between Riesz transforms and multiplication by $BMO(R^n)$-functions in the Schr\"odinger setting.