Lp-Boundedness of Wave Operators for¶Two Dimensional Schrödinger Operators
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- Yajima, K. Comm Math Phys (1999) 208: 125. doi:10.1007/s002200050751
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Let \(\) be the two dimensional Schrödinger operator with the real valued potential V which satisfies the decay condition at infinity \(\) for \(\). We show that the wave operators \(\), \(\), are bounded in \(\) for any 1<p<∞ under the condition that H has no zero bound states or zero resonance, extending the corresponding results for higher dimensions. As W± intertwine H0 and the absolutely continuous part H Pac of H : f(H)Pac=W±f(H0 )W±* for any Borel function f on ℝ1, this reduces the various Lp-mapping properties of f(H)Pac to those of f(H)0), the convolution operator by the Fourier transform of the function f(ξ2).