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On weighted boundedness and compactness of operators generated by fractional heat semigroups related with Schrödinger operators

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Abstract

Let \(L=-\Delta +V\) be a Schrödinger operator with the potential V belonging to the reverse Hölder class \(B_{q}, q>n/2\). Denote by \(\mathrm{CMO}_{\theta }(\rho )\) the vanishing mean oscillation type space associated with L. By the aid of the regularity estimates of the fractional heat kernel related with L, we investigate the weighted boundedness and compactness of the commutators of operators generated by fractional heat semigroups related to L and functions belonging to \(\mathrm{CMO}_{\theta }(\rho )\).

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Acknowledgements

The research is partially supported by the National Natural Science Foundation of China (Nos. 11871293, 11871452, 12071272 and 12071473) and Shandong Natural Science Foundation of China (Nos. ZR2020MA004 and ZR2017JL008).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qingdao University, Qingdao, 266071, Shandong, People’s Republic of China

    Tiantain Dai, Pengtao Li & Kai Zhao

  2. School of Applied Science, Beijing Information Science and Technology University, Beijing, 100192, People’s Republic of China

    Qianjun He

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  1. Tiantain Dai
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Correspondence to Pengtao Li.

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Communicated by Wenchang Sun.

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Dai, T., He, Q., Li, P. et al. On weighted boundedness and compactness of operators generated by fractional heat semigroups related with Schrödinger operators. Ann. Funct. Anal. 13, 77 (2022). https://doi.org/10.1007/s43034-022-00220-6

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