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arXiv · 1503.05747

Kato classes for Lévy processes

Tomasz Grzywny·Karol Szczypkowski
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Abstract

We prove that the definitions of the Kato class by the semigroup and by the resolvent of the Lévy process on $\mathbb{R}^d$ coincide if and only if 0 is not regular for {0}. If 0 is regular for {0} then we describe both classes in detail. We also give an analytic reformulation of these results by means of the characteristic (Lévy-Khintchine) exponent of the process. The result applies to the time-dependent (non-autonomous) Kato class. As one of the consequences we obtain a simultaneous time-space smallness condition equivalent to the Kato class condition given by the semigroup.

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BibTeXRIS

Tomasz Grzywny, Karol Szczypkowski. 2016-07-11. Kato classes for Lévy processes. https://doi.org/10.1007/s11118-017-9614-1

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