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Gradient estimates for Schrodinger operators with characterizations of BMO_{\mathcal{L}} on Heisenberg groups.
- Source :
-
Proceedings of the American Mathematical Society . May2023, Vol. 151 Issue 5, p2127-2142. 16p. - Publication Year :
- 2023
-
Abstract
- Let \mathcal {L}=-\Delta _{\mathbb {H}^n}+V be a Schrödinger operator with the nonnegative potential V belonging to the reverse Hölder class B_{Q}, where Q is the homogeneous dimension of the Heisenberg group \mathbb {H}^n. In this paper, we obtain pointwise bounds for the spatial derivatives of the heat and Poisson kernels related to \mathcal {L}. As an application, we characterize the space BMO_{\mathcal {L}}(\mathbb {H}^n), associated to the Schrödinger operator \mathcal {L}, in terms of two Carleson type measures involving the spatial derivatives of the heat kernel of the semigroup \{e^{-s\mathcal {L}}\}_{s>0} and the Poisson kernel of the semigroup \{e^{-s\sqrt {\mathcal {L}}}\}_{s>0}, respectively. At last, we pose a conjecture about the converse characterization of BMO_{\mathcal {L}}(\mathbb {H}^n). [ABSTRACT FROM AUTHOR]
- Subjects :
- *SCHRODINGER operator
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 151
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 162264441
- Full Text :
- https://doi.org/10.1090/proc/16308