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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2013; 50(5): 1009-1031

Printed September 1, 2013

https://doi.org/10.4134/JKMS.2013.50.5.1009

Copyright © The Korean Mathematical Society.

On estimates of Poisson kernels for symmetric L\'evy processes

Jaehoon Kang and Panki Kim

Seoul National University, Seoul National University

Abstract

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In this paper, using elementary calculus only, we give a simple proof that Green function estimates imply the sharp two-sided pointwise estimates for Poisson kernels for subordinate Brownian motions. In particular, by combining the recent result of Kim and Mimica \cite{KM2}, our result provides the sharp two-sided estimates for Poisson kernels for a large class of subordinate Brownian motions including geometric stable processes.

Keywords: symmetric L\'evy process, subordinate Brownian motion, Green function, Poisson kernel

MSC numbers: Primary 31B25, 60J75; Secondary 60J45, 60J50

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