Singular stochastic integral operators

Emiel Lorist; Mark Veraar

doi:10.2140/apde.2021.14.1443

Singular stochastic integral operators

Emiel Lorist^*, Mark Veraar

^*Corresponding author for this work

Analysis

Research output: Contribution to journal › Article › Scientific › peer-review

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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
Pages (from-to)	1443-1507
Number of pages	65
Journal	Analysis and PDE
Volume	14
Issue number	5
DOIs	https://doi.org/10.2140/apde.2021.14.1443
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-care
Otherwise 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

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title = "Singular stochastic integral operators",

abstract = "We introduce Calder{\'o}n-Zygmund theory for singular stochastic integrals with operator-valued kernel. In particular, we prove L p-extrapolation results under a H{\"o}rmander 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.",

keywords = "Calder{\'o}n-Zygmund theory, Muckenhoupt weights, singular stochastic integrals, sparse domination, stochastic maximal regularity, stochastic PDE",

author = "Emiel Lorist and Mark Veraar",

note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise 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. ",

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doi = "10.2140/apde.2021.14.1443",

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T1 - Singular stochastic integral operators

AU - Lorist, Emiel

AU - Veraar, Mark

N1 - 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-care Otherwise 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.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Calderón-Zygmund theory

KW - Muckenhoupt weights

KW - singular stochastic integrals

KW - sparse domination

KW - stochastic maximal regularity

KW - stochastic PDE

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DO - 10.2140/apde.2021.14.1443

M3 - Article

AN - SCOPUS:85116958859

SN - 2157-5045

VL - 14

SP - 1443

EP - 1507

JO - Analysis and PDE

JF - Analysis and PDE

IS - 5

ER -

Singular stochastic integral operators

Abstract

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