Vol. 14, No. 5, 2021

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Singular stochastic integral operators

Emiel Lorist and Mark Veraar

Vol. 14 (2021), No. 5, 1443–1507

We introduce Calderón–Zygmund theory for singular stochastic integrals with operator-valued kernel. In particular, we prove Lp-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 A2-conjecture. The results are applied to obtain p-independence and weighted bounds for stochastic maximal Lp-regularity both in the complex and real interpolation scale. As a consequence we obtain several new regularity results for the stochastic heat equation on d and smooth and angular domains.

singular stochastic integrals, stochastic maximal regularity, stochastic PDE, Calderón–Zygmund theory, Muckenhoupt weights, sparse domination
Mathematical Subject Classification
Primary: 60H15
Secondary: 35B65, 35R60, 42B37, 47D06
Received: 28 February 2019
Revised: 17 December 2019
Accepted: 9 February 2020
Published: 22 August 2021
Emiel Lorist
Delft Institute of Applied Mathematics
Delft University of Technology
Mark Veraar
Delft Institute of Applied Mathematics
Delft University of Technology