scholarly journals Atomic characterization of the Hardy space $H^1_L(\mathbb R)$ of one-dimensional Schrödinger operators with nonnegative potentials

2008 ◽  
Vol 136 (01) ◽  
pp. 89-95 ◽  
Author(s):  
Wojciech Czaja ◽  
Jacek Zienkiewicz
Keyword(s):  
Hardy Space ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional

scholarly journals Area Integral Characterization of Hardy space H1L related to Degenerate Schrödinger Operators

2019 ◽  
Vol 9 (1) ◽  
pp. 1291-1314
Author(s):  
Jizheng Huang ◽  
Pengtao Li ◽  
Yu Liu
Keyword(s):  
Hardy Space ◽  
Schrödinger Operators ◽  
Heat Semigroup ◽  
Schrodinger Operators ◽  
Reverse Hölder Class ◽  
Area Integral ◽  
Muckenhoupt Class ◽  
Degenerate Schrödinger Operator ◽  
Reverse Hölder

Abstract Let $$\begin{array}{} \displaystyle Lf(x)=-\frac{1}{\omega(x)}\sum_{i,j}^{}\partial_{i}(a_{ij}(\cdot)\partial_{j}f)(x)+V(x)f(x) \end{array}$$ be the degenerate Schrödinger operator, where ω is a weight from the Muckenhoupt class A2, V is a nonnegative potential that belongs to a certain reverse Hölder class with respect to the measure ω(x)dx. For such an operator we define the area integral $\begin{array}{} \displaystyle S^{L}_h \end{array}$ associated with the heat semigroup and obtain the area integral characterization of $\begin{array}{} \displaystyle H^{1}_{L} \end{array}$, which is the Hardy space associated with L.

scholarly journals Reflection Probabilities of One-Dimensional Schrödinger Operators and Scattering Theory

2017 ◽  
Vol 18 (6) ◽  
pp. 2075-2085 ◽  
Author(s):  
Benjamin Landon ◽  
Annalisa Panati ◽  
Jane Panangaden ◽  
Justine Zwicker
Keyword(s):  
Scattering Theory ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
One Dimensional
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