Quantitative Boundedness of Littlewood--Paley Functions on Weighted Lebesgue Spaces in the Schr\"{o}dinger Setting.

@article{Zhang2019QuantitativeBO,
  title={Quantitative Boundedness of Littlewood--Paley Functions on Weighted Lebesgue Spaces in the Schr\"\{o\}dinger Setting.},
  author={J. Zhang and Dachun Yang},
  journal={arXiv: Classical Analysis and ODEs},
  year={2019}
}
Let $L:=-\Delta+V$ be the Schrodinger operator on $\mathbb{R}^n$ with $n\geq 3$, where $V$ is a non-negative potential which belongs to certain reverse Holder class $RH_q(\mathbb{R}^n)$ with $q\in (n/2,\,\infty)$. In this article, the authors obtain the quantitative weighted boundedness of Littlewood--Paley functions $g_L$, $S_L$ and $g_{L,\,\lambda}^\ast$, associated to $L$, on weighted Lebesgue spaces $L^p(w)$, where $w$ belongs to the class of Muckenhoupt $A_p$ weights adapted to $L$. 

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