Singular stochastic integral operators

Journal article (2021)

Authors

E. Lorist Analysis - EEMCS
M.C. Veraar Analysis - EEMCS
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2021 E. Lorist, M.C. Veraar
DOI
help_outline
https://doi.org/10.2140/apde.2021.14.1443
Muckenhoupt weights Calderón-Zygmund theory Singular stochastic integrals Sparse domination Stochastic maximal regularity Stochastic PDE
More Info
expand_more

Published Date

2021

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

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.

Files

SSIO.pdf
(.pdf | 0.892 Mb)