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Regularities of semigroups, Carleson measures and the characterizations of BMO-type spaces associated with generalized Schrödinger operators. (English) Zbl 1405.42021

Summary: Let \(\mathcal{L}=-\Delta+\mu\) be the generalized Schrödinger operator on \(\mathbb{R}^{n}\), \(n\geq3\), where \(\Delta\) is the Laplacian and \(\mu\) not \(\equiv0\) is a nonnegative Radon measure on \(\mathbb{R}^{n}\). In this article, we introduce two families of Carleson measures \(\{d\nu_{h,k}\}\) and \(\{d\nu_{P,k}\}\) generated by the heat semigroup \(\{e^{-t\mathcal{L}}\}\) and the Poisson semigroup \(\{e^{-t\sqrt{\mathcal{L}}}\}\), respectively. By the regularities of semigroups, we establish the Carleson measure characterizations of BMO-type spaces \(\text{BMO}_{\mathcal{L}}(\mathbb{R}^{n})\) associated with the generalized Schrödinger operators.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B30 \(H^p\)-spaces
35J10 Schrödinger operator, Schrödinger equation
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References:

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