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- W2609661611 abstract "In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive noises bess du_t(x)=Delta^{frac{alpha}{2}}u_t(x)dt+sum_{k=1}^inftyint_{mathbb{R}^m}g^k(t,x)ztilde N_k(dz,dt), u_0=0, 0leq tleq T, eess where $Delta^{frac{alpha}{2}}=-(-Delta)^{frac{alpha}{2}}$, and $int_{mathbb{R}^m}ztilde N_k(t,dz)=:Y_t^k$ are independent $m$-dimensional pure jump Levy processes with Levy measure of $nu^k$. Following the idea of cite{Kim}, we obtain the $q$-th order BMO quasi-norm of the $frac{alpha}{q_0}$-order derivative of $u$ is controlled by the norm of $g$." @default.
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- W2609661611 date "2017-04-19" @default.
- W2609661611 modified "2023-09-27" @default.
- W2609661611 title "BMO estimates for stochastic singular integral operators and its application to PDEs with L'{e}vy noise" @default.
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