Singular stochastic integral operators

Journal article (2021)

Authors

E. Lorist Analysis -

M.C. Veraar Analysis -

Research Group

Analysis () (TU Delft)

DOI: https://doi.org/10.2140/apde.2021.14.1443

Muckenhoupt weights Calderón-Zygmund theory Singular stochastic integrals Sparse domination Stochastic maximal regularity Stochastic PDE

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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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.

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