Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2022; 59(2): 235-254

Published online March 1, 2022 https://doi.org/10.4134/JKMS.j200484

Copyright © The Korean Mathematical Society.

Hardy type estimates for Riesz transforms associated with Schr\"{o}dinger operators on the Heisenberg group

Chunfang Gao

Qingdao University

Abstract

Let $\mathbb{H}^{n}$ be the Heisenberg group and $Q=2n+2$ be its homogeneous dimension. Let $\mathcal{L}=-\Delta_{\mathbb{H}^{n}}+V$ be the Schr\"{o}dinger operator on $\mathbb{H}^{n}$, where $\Delta_{\mathbb{H}^{n}}$ is the sub-Laplacian and the nonnegative potential $V$ belongs to the reverse H\"{o}lder class $B_{q_{1}}$ for $q_{1}\geq Q/2$. Let ${H_{\mathcal{L}}^{p}(\mathbb{H}^{n})}$ be the Hardy space associated with the Schr\"{o}dinger operator $\mathcal{L}$ for $Q/(Q+\delta_{0})

Keywords: Heisenberg group, Schr\"{o}dinger operator, Riesz transform, commutator

MSC numbers: Primary 42B20, 42B35

Supported by: This work was financially supported by Shandong Natural Science Foundation of Chian ZR2017JL008.