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2021 Singular stochastic integral operators
Emiel Lorist, Mark Veraar
Anal. PDE 14(5): 1443-1507 (2021). DOI: 10.2140/apde.2021.14.1443

Abstract

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.

Citation

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Emiel Lorist. Mark Veraar. "Singular stochastic integral operators." Anal. PDE 14 (5) 1443 - 1507, 2021. https://doi.org/10.2140/apde.2021.14.1443

Information

Received: 28 February 2019; Revised: 17 December 2019; Accepted: 9 February 2020; Published: 2021
First available in Project Euclid: 6 January 2022

Digital Object Identifier: 10.2140/apde.2021.14.1443

Subjects:
Primary: 60H15
Secondary: 35B65 , 35R60 , 42B37 , 47D06

Keywords: Calderón–Zygmund theory , Muckenhoupt weights , singular stochastic integrals , sparse domination , stochastic maximal regularity , Stochastic pde

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 5 • 2021
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