TWO-WEIGHT NORM ESTIMATES FOR SQUARE FUNCTIONS ASSOCIATED TO FRACTIONAL SCHRÖDINGER OPERATORS WITH HARDY POTENTIAL

Let $d\in\mathbb{N}$ and ${\alpha}\in(0,\min\{2,d\})$. For any $a\in[a^\ast,\infty)$, the fractional Schr\"odinger operator $\mathcal{L}_a$ is defined by \begin{equation*} \mathcal{L}_a:=(-\Delta)^{{\alpha}/2}+a{|x|}^{-{\alpha}}, \end{equation*} where $a^*:=-{\frac{2^{\alpha}{\Gamma}((d+{\alpha...

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Bibliographic Details
Published in:Taehan Suhakhoe hoebo 2023, 60(6), , pp.1567-1605
Main Authors: Tongxin Kang, Yang Zou
Format: Article
Language:English
Subjects:
수학
Online Access:Get full text
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Summary:Let $d\in\mathbb{N}$ and ${\alpha}\in(0,\min\{2,d\})$. For any $a\in[a^\ast,\infty)$, the fractional Schr\"odinger operator $\mathcal{L}_a$ is defined by \begin{equation*} \mathcal{L}_a:=(-\Delta)^{{\alpha}/2}+a{|x|}^{-{\alpha}}, \end{equation*} where $a^*:=-{\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}((d-{\alpha})/4)^2}}$. In this paper, we study two-weight Sobolev inequalities associated with $\mathcal{L}_a$ and two-weight norm estimates for several square functions associated with $\mathcal{L}_a$. KCI Citation Count: 0
ISSN:1015-8634
2234-3016
DOI:10.4134/BKMS.b220752