Weighted inequalities for variation operators associated with fractional Schrödinger semigroups

Key Points

• The study finds weighted boundedness properties for the variation operator associated with fractional Schrödinger semigroups, improving existing inequalities.
• Key evidence includes the development of a new class of weighted Lp-Lq quantitative inequalities linking various function spaces in the analysis.
• Assessment shows that the operators exhibit mixed weak-type inequalities under the framework of reverse Hölder classes, enhancing mathematical understanding.
• The implications are noteworthy, as they provide groundwork for further research in spectral theory and functional analysis.