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Commutators of BMO functions and degenerate Schrödinger operators with certain nonnegative potentials. (English) Zbl 1236.42016

Summary: Let f(x)=-1 ω i,j i (a i,j (·) j f)(x)+V(x)f(x) with the non-negative potential V belonging to the reverse Hölder class with respect to the measure ω(x)dx, where ω(x) satisfies the A 2 condition of Muckenhoupt and let a i,j (x) be a real symmetric matrix satisfying

λ -1 ω(x)|ξ| 2 i,j=1 n a i,j (x)ξ i ξ j λω(x)|ξ| 2 ·

We obtain some estimates for V α -α on the weighted L p spaces and we study the weighted L p boundedness of the commutator [b,V α -α ] when bBMO ω and 0<α1.

MSC:
42B30H p -spaces (Fourier analysis)
35J10Schrödinger operator
References:
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