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 |
|---|---|
| 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.
In: Journal of Functional Analysis, Vol. 269, No. 5, 01.09.2015, p. 1289-1309.Research output: Contribution to journal › Article
}
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
VL - 269
SP - 1289
EP - 1309
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 5
ER -