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L p estimates for Schrödinger operators with certain potentials. (English) Zbl 0818.35021
Summary: We consider the Schrödinger operators -Δ+V(x) in n where the nonnegative potential V(x) belongs to the reverse Hölder class B q for some qn2. We obtain the optimal L p estimates for the operators (-Δ+V) iγ , 2 (-Δ+V) -1 ,(-Δ+V) -12 and (-Δ+V) -1 where γ. In particular we show that (-Δ+V) iγ is a Calderón-Zygmund operator if VB n2 and (-Δ+V) -12 ,(-Δ+V) -1 are Calderón-Zygmund operators if VB n .

35J10Schrödinger operator
42B20Singular and oscillatory integrals, several variables