### 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 language | English |
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Pages (from-to) | 1289-1309 |

Number of pages | 21 |

Journal | Journal of Functional Analysis |

Volume | 269 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2015 Sep 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Analysis

### Cite this

**A BMO estimate for stochastic singular integral operators and its application to SPDEs.** / Kim, Ildoo.

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 269, no. 5, pp. 1289-1309. https://doi.org/10.1016/j.jfa.2015.05.015

}

TY - JOUR

T1 - A BMO estimate for stochastic singular integral operators and its application to SPDEs

AU - Kim, Ildoo

PY - 2015/9/1

Y1 - 2015/9/1

N2 - 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∞.

AB - 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∞.

KW - BMO (bounded mean oscillation) estimates

KW - Stochastic partial differential equations

KW - Stochastic singular integral operator

UR - http://www.scopus.com/inward/record.url?scp=84937515472&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937515472&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2015.05.015

DO - 10.1016/j.jfa.2015.05.015

M3 - Article

AN - SCOPUS:84937515472

VL - 269

SP - 1289

EP - 1309

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 5

ER -