Abstract
In this paper, we obtain sharp two-sided estimates of Poisson kernels for pure jump symmetric Lévy processes in C1,1 open sets. In particular, by combining Green function estimates obtained by Kim and Mimica (Electron. J. Probab., 23(64), 1–45, 2018), our result covers subordinate Brownian motions with high intensity of small jumps such as conjugate geometric stable process whose Laplace exponent is \(\lambda \mapsto \lambda /(\log (1+\lambda ^{\alpha /2}))\) for 0 < α < 2. As an application, we show the existence of tangential limits for harmonic functions in C1,1 open sets.
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28 February 2024
A Correction to this paper has been published: https://doi.org/10.1007/s11118-024-10121-z
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This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. NRF-2019R1A5A1028324).
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Kang, J. Estimates of Poisson Kernels for Symmetric Lévy Processes and Their Applications. Potential Anal 60, 1–25 (2024). https://doi.org/10.1007/s11118-022-10042-9
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DOI: https://doi.org/10.1007/s11118-022-10042-9
Keywords
- Symmetric Lévy process
- Subordinate Brownian motion
- Poisson kernel
- Harmonic function
- Boundary Harnack principle
- Tangential limits