A BMO estimate for stochastic singular integral operators and its application to SPDEs

作者：Kim Ildoo^*

来源：Journal of Functional Analysis, 2015, 269(5): 1289-1309.

DOI：10.1016/j.jfa.2015.05.015

• Stochastic singular integral operator
• Stochastic partial differential
• equations BMO (bounded mean oscillation)
• estimates

In this paper, we investigate kernel conditions on K(t,s,infinity) so that the stochastic singular integral operator integral K-t(0)(t,s,.)*g(s,.)(x) dw(s) has a bounded mean oscillation. As an application we prove that for the solution u of the stochastic heat equation
du(t) (x) = a(ij)(t)u(x)i(x)jdt + g(t)(k)(x)dw(t)(k)), u(0)= 0 t <= T (0.1)
the q-th order BMO quasi-norm of the derivatives of u is controlled by parallel to g parallel to L-infinity.

• 出版日期2015-9-1