Abstract
In this paper, we consider the boundedness of the differential transforms for the generalized Poisson operators associated with the Laplace operator \(\Delta \). The related results of the differential transforms for the heat semigroup are proved previously. By using the subordination formula method, we prove the boundedness of the maximal operator related to the differential transforms in weighted Lebesgue spaces. Moreover, we get some \(L^\infty \)-behavior results and the local growth of the maximal operator related to the differential transforms. Also, we get some similar results of the differential transforms related to the generalized Poisson operators generated by Schrödinger operator \(-\Delta +V\), where the nonnegative potential V belongs to the reverse Hölder class \(B_q\) with \(q\ge n/2.\)
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Communicated by Rosihan M. Ali.
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Supported by the National Natural Science Foundation of China (Grant No. 11971431) and the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY22A010011).
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Lei, H., Wen, K. & Zhang, C. Boundedness of the differential transforms for the generalized Poisson operators generated by Laplacian. Bull. Malays. Math. Sci. Soc. 46, 145 (2023). https://doi.org/10.1007/s40840-023-01542-x
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DOI: https://doi.org/10.1007/s40840-023-01542-x