The characterizations of Hardy-Sobolev spaces by fractional square functions related to Schrödinger operators. (English) Zbl 1446.42034
Summary: Let \(L = -\Delta + V\) be a Schrödinger operator, where the potential \(V\) satisfies the reverse Hölder condition. In this paper, via the heat semigroup \(e^{-tL}\) and the Poisson semigroup \(e^{-t\sqrt{L}}\), we introduce several classes of fractional square functions associated with \(L\) including the Litttlewood-Paley \(g\)-function, the area integral and the \(g_\lambda^*\)-function, respectively. By the regularities of semigroup, we establish several square function characterizations of the Hardy space and the Hardy-Sobolev space related to the Schrödinger operator.
MSC:
| 42B35 | Function spaces arising in harmonic analysis |
| 47A60 | Functional calculus for linear operators |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 35J10 | Schrödinger operator, Schrödinger equation |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
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