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arXiv · 1302.5053

Parabolic Littlewood-Paley inequality for $\phi(-\Delta)$-type operators and applications to Stochastic integro-differential equations

Ildoo Kim·Kyeong-Hun Kim·Panki Kim
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Abstract

In this paper we prove a parabolic version of the Littlewood-Paley inequality for the operators of the type $\phi(-\Delta)$, where $\phi$ is a Bernstein function. As an application, we construct an $L_p$-theory for the stochastic integro-differential equations of the type $du=(-\phi(-\Delta)u+f)dt +gdW_t$.

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Ildoo Kim, Kyeong-Hun Kim, Panki Kim. 2013-02-20. Parabolic Littlewood-Paley inequality for $\phi(-\Delta)$-type operators and applications to Stochastic integro-differential equations. https://arxiv.org/abs/1302.5053

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