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The Commutators of Bochner–Riesz Operators for Hermite Operator

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Abstract

In this paper, we study the \(L^p\)-boundedness of the commutator \( [b, S_R^\delta (H)](f) = bS_R^\delta (H) f - S_R^\delta (H)(bf) \) of a BMO function b and the Bochner–Riesz means \(S_R^\delta (H)\) for Hermite operator \(H=-\Delta +|x|^2\) on \({\mathbb {R}}^n\), \(n\ge 2\). We show that if \(\delta >\delta (q)=n(1/q -1/2)- 1/2\), the commutator \([b,S_R^\delta (H)]\) is bounded on \(L^p({\mathbb {R}}^n)\) whenever \(q<p<q'\) and \(1\le q\le 2n/ (n+2)\).

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Acknowledgements

P. Chen, X. Lin and L. Yan were supported by National Key R &D Program of China 2022YFA1005700. P. Chen was supported by NNSF of China 12171489 and Guangdong Natural Science Foundation 2022A1515011157. L. Yan was supported by the NNSF of China 11871480 and by the Australian Research Council (ARC) through the research Grant DP190100970.

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  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Peng Chen, Xixi Lin & Lixin Yan

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  1. Peng Chen
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Correspondence to Xixi Lin.

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Chen, P., Lin, X. & Yan, L. The Commutators of Bochner–Riesz Operators for Hermite Operator. J Geom Anal 33, 87 (2023). https://doi.org/10.1007/s12220-022-01137-1

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