Singular stochastic integral operators
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Abstract
We introduce Calderón-Zygmund theory for singular stochastic integrals with operator-valued kernel. In particular, we prove L p-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 L p-regularity both in the complex and real interpolation scale. As a consequence we obtain several new regularity results for the stochastic heat equation on (Formula presented) and smooth and angular domains.