PreprintCC BY 4.0arXiv
Lp-extrapolation via non-local decay estimates: theory and applications to the generalized Stokes operator with rough coefficients
Abstract
In this article, we establish Lp-mapping properties for the generalized Stokes operator with bounded measurable coefficients on the full range of exponents that is known to be sharp for elliptic systems with rough coefficients. These include Lp-estimates for the corresponding semigroup, its gradient and the H∞-calculus, as well as Lq-Lp smoothing estimates. As a key ingredient, we develop a non-local framework for Lp-extrapolation that captures the relationship between hypercontractivity, non-local decay estimates and uniform Łp-bounds.
Related
- Weighted Lq-Lr estimates of a generalized Oseen evolution operator in exterior domains, with applications to the Navier-Stokes flow past a rigid body
- Gradient estimates for generalized double phase problems with two modulating coefficients
- Into the danger zone: stable extrapolation in high-dimensional function and operator learning
- Extrapolation of extreme covariates in generalized additive regression using extreme value theory
- Sharp maximum estimates for linear uniformly elliptic equations with measurable coefficients
BibTeX
@misc{haardt2026lpextrapolation,
title = {{$\mathrmL^p$-extrapolation via non-local decay estimates: theory and applications to the generalized Stokes operator with rough coefficients}},
author = {Luca Haardt},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10427},
eprint = {2609.10427},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10427},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - L^p-extrapolation via non-local decay estimates: theory and applications to the generalized Stokes operator with rough coefficients
AU - Luca Haardt
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.10427
UR - https://arxiv.org/abs/2609.10427
AB - In this article, we establish L^p-mapping properties for the generalized Stokes operator with bounded measurable coefficients on the full range of exponents that is known to be sharp for elliptic systems with rough coefficients. These include L^p-estimates for the corresponding semigroup, its gradient and the H^∞-calculus, as well as L^q-L^p smoothing estimates. As a key ingredient, we develop a non-local framework for L^p-extrapolation that captures the relationship between hypercontractivity, non-local decay estimates and uniform Ł^p-bounds.
ER -