Regularity of the generalized Poisson operator. (English) Zbl 1483.42015
Summary: Let \(L=-\Delta +V\) be a Schrödinger operator, where the potential \(V\) belongs to the reverse Hölder class. In this paper, by the subordinative formula, we investigate the generalized Poisson operator \(P^L_{t,\sigma}\), \(0<\sigma<1\), associated with \(L\). We estimate the gradient and the time-fractional derivatives of the kernel of \(P^L_{t,\sigma}\), respectively. As an application, we establish a Carleson measure characterization of the Campanato type space \(\mathcal{C}^{\gamma}_L(\mathbb{R}^n)\) via \(P^L_{t,\sigma} \).
MSC:
| 42B35 | Function spaces arising in harmonic analysis |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 42B37 | Harmonic analysis and PDEs |
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