Banach Journal of Mathematical Analysis

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

Yuanyuan Hao, Pengtao Li, and Kai Zhao

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Let L=Δ+μ be the generalized Schrödinger operator on Rn,n3, where Δ is the Laplacian and μ0 is a nonnegative Radon measure on Rn. In this article, we introduce two families of Carleson measures {dνh,k} and {dνP,k} generated by the heat semigroup {etL} and the Poisson semigroup {etL}, respectively. By the regularities of semigroups, we establish the Carleson measure characterizations of BMO-type spaces BMOL(Rn) associated with the generalized Schrödinger operators.

Article information

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

Received: 10 March 2018
Accepted: 13 April 2018
First available in Project Euclid: 15 October 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B30: $H^p$-spaces 35J10: Schrödinger operator [See also 35Pxx]

generalized Schrödinger operator Carleson measure BMO-type space regularity of semigroup


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.

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