@article{Wang2023, 
author = {Zhiyong Wang and Kai Zhao and Pengtao Li and Yu Liu},
title = {Boundedness of square functions related with fractional Schrödinger semigroups on stratified Lie groups},
year = {2023},
journal = {Communications in Analysis and Mechanics},
volume = {15},
number = {3},
pages = {410-435},
keywords = {Schrödinger operators, Morrey spaces, Carleson measures, fractional heat semigroups, Campanato spaces},
url = {https://www.sciopen.com/article/10.3934/cam.2023020},
doi = {10.3934/cam.2023020},
abstract = {In this paper, we consider a Schrödinger operator    L  =  −      Δ                  H              +  V on the stratified Lie group        H  . First, we establish fractional heat kernel estimates related to        L          β      ,    β  ∈  (  0  ,  1  ). By utilizing kernel estimations and the fractional Carleson measure, we are able to derive a characterization of the Campanato type space    B  M      O          L              v        (      H    ). Second, we demonstrate that both Littlewood-Paley        g  -functions and area functions are bounded on    B  M      O          L              v        (      H    ). Finally, we also obtain that the above square functions are bounded on the Morrey space        L          p      ,      κ              γ      ,      θ        (      H    ) and the weak Morrey space    W      L          1      ,      κ              γ      ,      θ        (      H    ), respectively.}
}