The Stokes Operator with Power Weights Outside the Muckenhoupt Class

Erik S. Heidrich

The Stokes Operator with Power Weights Outside the Muckenhoupt Class

Analysis of PDEs 2026-06-30 v1

Authors: Erik S. Heidrich

Abstract

In this paper, we prove estimates for the Stokes resolvent problem with no-slip boundary conditions on the half space in weighted $L^p$ -spaces. The weights we consider are power weights both inside and outside the Muckenhoupt range. Our estimates imply that the corresponding Stokes operator is the generator of a bounded analytic $C_0$ -semigroup. We furthermore show that it admits a bounded $H^\infty$ -calculus of angle $0.$ This results seems to be new even within the Muckenhoupt range.

Keywords

Stokes operator power weights Muckenhoupt class analytic semigroup H∞-calculus half space

Cite

@article{arxiv.2606.31542,
  title  = {The Stokes Operator with Power Weights Outside the Muckenhoupt Class},
  author = {Erik S. Heidrich},
  journal= {arXiv preprint arXiv:2606.31542},
  year   = {2026}
}

Comments

16 pages, no figures