Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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REGULARITY OF THE GENERALIZED POISSON OPERATOR

  • Li, Pengtao (School of Mathematics and Statistics Qingdao University) ;
  • Wang, Zhiyong (School of Mathematics and Statistics Qingdao University) ;
  • Zhao, Kai (School of Mathematics and Statistics Qingdao University)
  • Received : 2021.04.03
  • Accepted : 2021.09.24
  • Published : 2022.01.01
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Abstract

Let L = -∆ + V be a Schrödinger operator, where the potential V belongs to the reverse Hölder class. In this paper, by the subordinative formula, we investigate the generalized Poisson operator PLt,σ, 0 < σ < 1, associated with L. We estimate the gradient and the time-fractional derivatives of the kernel of PLt,σ, respectively. As an application, we establish a Carleson measure characterization of the Campanato type space 𝒞𝛄L (ℝn) via PLt,σ.

Keywords

Acknowledgement

This work was financially supported by the National Natural Science Foundation of China (No. 12071272) and Shandong Natural Science Foundation of China (Nos. ZR2020MA004, ZR2017JL008).

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