On Lp boundedness of wave operators for 4-dimensional Schrodinger operators with threshold singularities |
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Authors: | Jensen, Arne Yajima, Kenji |
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Affiliation: | Department of Mathematical Sciences Aalborg University, Fredrik Bajers Vej 7G DK-9220 Aalborg Ø Denmark |
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Abstract: | Let H=–+V(x) be a Schrödinger operator on L2(R4),H0=–. Assume that |V(x)|+| V(x)|C x – for some>8. Let be the wave operators. It is known that W± extend to bounded operators in Lp(R4)for all 1p, if 0 is neither an eigenvalue nor a resonance ofH. We show that if 0 is an eigenvalue, but not a resonance ofH, then the W± are still bounded in Lp(R4) for all psuch that 4/3<p<4. |
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