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

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5 Citations (Scopus)

Abstract

In this paper, we investigate kernel conditions on K(. t, s, x) so that the stochastic singular integral operator ∫0tK(t,s,{dot operator})*g(s,{dot operator})(x)dws has a bounded mean oscillation. As an application, we prove that for the solution u of the stochastic heat equation. (0.1)dut(x)=aij(t)uxixjdt+gtk(x)dwtk,u0=0,t≤T, the q-th order BMO quasi-norm of the derivatives of u is controlled by {norm of matrix}g{norm of matrix}L∞.

Original languageEnglish
Pages (from-to)1289-1309
Number of pages21
JournalJournal of Functional Analysis
Volume269
Issue number5
DOIs
Publication statusPublished - 2015 Sep 1

Keywords

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

ASJC Scopus subject areas

  • Analysis

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