Mixed inequalities for operators associated to critical radius functions with applications to Schrödinger type operators. (English) Zbl 1531.42023
Summary: We obtain weighted mixed inequalities for operators associated to a critical radius function. We consider Schrödinger Calderón-Zygmund operators of \((s, \delta )\) type, for \(1<s\leq \infty\) and \(0 < \delta \leq 1\). We also give estimates of the same type for the associated maximal operators. As an application, we obtain a wide variety of mixed inequalities for Schrödinger type singular integrals. As far as we know, these results are a first approach of mixed inequalities in the Schrödinger setting.
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 35J10 | Schrödinger operator, Schrödinger equation |
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