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

Ildoo Kim

doi:10.1016/j.jfa.2015.05.015

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

Ildoo Kim

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1289-1309
Number of pages	21
Journal	Journal of Functional Analysis
Volume	269
Issue number	5
DOIs	https://doi.org/10.1016/j.jfa.2015.05.015
Publication status	Published - 2015 Sep 1

Keywords

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

ASJC Scopus subject areas

Analysis

Access to Document

10.1016/j.jfa.2015.05.015

Fingerprint Dive into the research topics of 'A BMO estimate for stochastic singular integral operators and its application to SPDEs'. Together they form a unique fingerprint.

Cite this

@article{c101baeb3ea14663bd4a2887341dce43,

title = "A BMO estimate for stochastic singular integral operators and its application to SPDEs",

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∞.",

keywords = "BMO (bounded mean oscillation) estimates, Stochastic partial differential equations, Stochastic singular integral operator",

author = "Ildoo Kim",

year = "2015",

month = sep,

day = "1",

doi = "10.1016/j.jfa.2015.05.015",

language = "English",

volume = "269",

pages = "1289--1309",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "5",

}

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 -