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.
Original language | English |
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Pages (from-to) | 1443-1507 |
Number of pages | 65 |
Journal | Analysis and PDE |
Volume | 14 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2021 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- Calderón-Zygmund theory
- Muckenhoupt weights
- singular stochastic integrals
- sparse domination
- stochastic maximal regularity
- stochastic PDE