Singular stochastic integral operators

Lorist, Emiel; Veraar, Mark

doi:10.2140/apde.2021.14.1443

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

Singular stochastic integral operators

Emiel Lorist and Mark Veraar

Vol. 14 (2021), No. 5, 1443–1507

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 $L^{p}$ -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 $A_{2}$ -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 $ℝ^{d}$ and smooth and angular domains.

Keywords

singular stochastic integrals, stochastic maximal regularity, stochastic PDE, Calderón–Zygmund theory, Muckenhoupt weights, sparse domination

Mathematical Subject Classification

Primary: 60H15

Secondary: 35B65, 35R60, 42B37, 47D06

Milestones

Received: 28 February 2019

Revised: 17 December 2019

Accepted: 9 February 2020

Published: 22 August 2021

Authors

Emiel Lorist
Delft Institute of Applied Mathematics Delft University of Technology Delft Netherlands

Mark Veraar
Delft Institute of Applied Mathematics Delft University of Technology Delft Netherlands

Vol. 14, No. 5, 2021