Weighted inequalities for negative powers of Schrödinger operators
Let \(L=-\Delta +V\) be the Schrödinger operator on \(\mathbb R^d\), \(d\geq 3\), where \(V\geq 0\) is a function satisfying for some \(q\geq d/2\) the reverse Hölder inequality \[ \left (\frac{1}{| B| } \int_B V(y) ^q \,dy \right )^{1/q} \leq \frac{C}{| B| } \int_B V(y) \,dy \] for every ball \(B\) in \(\mathbb R^d\). The paper deals with the operator \(I_\alpha =L^{-\alpha/2}\), \(\alpha >0\), the action of which is considered on weighted weak \(L^p\) spaces and on a certain new class of BMO spaces. New boundedness and characterization results are obtained.
scientific article; zbMATH DE number 5349064
scientific article