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

Department of Mathematics

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

6 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 Sept 1

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

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

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2015.05.015

Cite this

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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∞.",

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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

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SP - 1289

EP - 1309

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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