Abstract
We introduce Calderón–Zygmund theory for singular stochastic integrals with operator-valued kernel. In particular, we prove -extrapolation results under a Hörmander condition on the kernel. Sparse domination and sharp weighted bounds are obtained under a Dini condition on the kernel, leading to a stochastic version of the solution to the -conjecture. The results are applied to obtain -independence and weighted bounds for stochastic maximal -regularity both in the complex and real interpolation scale. As a consequence we obtain several new regularity results for the stochastic heat equation on and smooth and angular domains.
Citation
Emiel Lorist. Mark Veraar. "Singular stochastic integral operators." Anal. PDE 14 (5) 1443 - 1507, 2021. https://doi.org/10.2140/apde.2021.14.1443
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