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• W2624444348 abstract "Let $H=-Delta+V$ be a Schrodinger operator on $L^2(mathbb R^2)$ with real-valued potential $V$, and let $H_0=-Delta$. If $V$ has sufficient pointwise decay, the wave operators $W_{pm}=s-lim_{tto pminfty} e^{itH}e^{-itH_0}$ are known to be bounded on $L^p(mathbb R^2)$ for all $1< p< infty$ if zero is not an eigenvalue or resonance. We show that if there is an s-wave resonance or an eigenvalue only at zero, then the wave operators are bounded on $L^p(mathbb R^2)$ for $1 < p<infty$. This result stands in contrast to results in higher dimensions, where the presence of zero energy obstructions is known to shrink the range of valid exponents $p$." @default.
• W2624444348 created "2017-06-15" @default.
• W2624444348 creator A5011150158 @default.
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• W2624444348 date "2018-04-01" @default.
• W2624444348 modified "2023-10-15" @default.
• W2624444348 title "On the L boundedness of wave operators for two-dimensional Schrödinger operators with threshold obstructions" @default.
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• W2624444348 doi "https://doi.org/10.1016/j.jfa.2017.12.001" @default.
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