We obtain the quantitative weighted strong-type and weak-type estimates for variation operators associated with heat semigroups in the Schrödinger setting. In particular, we first established the quantitative endpoint bound for such operators in the Schrödinger setting, which is the main novelty of our results.
"QUANTITATIVE WEIGHTED BOUNDS FOR VARIATION OPERATORS ASSOCIATED WITH HEAT SEMIGROUPS IN THE SCHRÖDINGER SETTING." Rocky Mountain J. Math. 53 (5) 1645 - 1656, October 2023. https://doi.org/10.1216/rmj.2023.53.1645