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http://dx.doi.org/10.4134/JKMS.j210224

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)
Publication Information
Journal of the Korean Mathematical Society / v.59, no.1, 2022 , pp. 129-150 More about this Journal
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
Regularities; Schrodinger operators; the generalized Poisson operators; Campanato type spaces;
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