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A BMO estimate for stochastic singular integral operators and its application to SPDEs
- Authors
- Kim, Ildoo
- Issue Date
- 1-9월-2015
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Stochastic singular integral operator; Stochastic partial differential; equations BMO (bounded mean oscillation); estimates
- Citation
- JOURNAL OF FUNCTIONAL ANALYSIS, v.269, no.5, pp.1289 - 1309
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF FUNCTIONAL ANALYSIS
- Volume
- 269
- Number
- 5
- Start Page
- 1289
- End Page
- 1309
- ISSN
- 0022-1236
- Abstract
- In this paper, we investigate kernel conditions on K(t,s,infinity) so that the stochastic singular integral operator integral K-t(0)(t,s,.)*g(s,.)(x) dw(s) has a bounded mean oscillation. As an application we prove that for the solution u of the stochastic heat equation du(t) (x) = a(ij)(t)u(x)i(x)jdt + g(t)(k)(x)dw(t)(k)), u(0)= 0 t <= T (0.1) the q-th order BMO quasi-norm of the derivatives of u is controlled by parallel to g parallel to L-infinity. (C) 2015 Elsevier Inc. All rights reserved.
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