## Banach Journal of Mathematical Analysis

### Regularities of semigroups, Carleson measures and the characterizations of BMO-type spaces associated with generalized Schrödinger operators

#### Abstract

Let $\mathcal{L}=-\Delta+\mu$ be the generalized Schrödinger operator on $\mathbb{R}^{n},n\geq3$, where $\Delta$ is the Laplacian and $\mu\notequiv0$ 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 $\mathrm{BMO}_{\mathcal{L}}(\mathbb{R}^{n})$ associated with the generalized Schrödinger operators.

#### Article information

Source
Banach J. Math. Anal., Volume 13, Number 1 (2019), 1-25.

Dates
Accepted: 13 April 2018
First available in Project Euclid: 15 October 2018

https://projecteuclid.org/euclid.bjma/1539590538

Digital Object Identifier
doi:10.1215/17358787-2018-0013

Mathematical Reviews number (MathSciNet)
MR3895004

Zentralblatt MATH identifier
07002029

#### Citation

Hao, Yuanyuan; Li, Pengtao; Zhao, Kai. Regularities of semigroups, Carleson measures and the characterizations of BMO-type spaces associated with generalized Schrödinger operators. Banach J. Math. Anal. 13 (2019), no. 1, 1--25. doi:10.1215/17358787-2018-0013. https://projecteuclid.org/euclid.bjma/1539590538

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