Parabolic Littlewood-Paley inequality for $ϕ(-Δ)$-type operators and applications to Stochastic integro-differential equations

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

No reviews yet.

No comments yet.