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arXiv · 2606.31542

The Stokes Operator with Power Weights Outside the Muckenhoupt Class

Erik S. Heidrich
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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.

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Erik S. Heidrich. 2026-06-30. The Stokes Operator with Power Weights Outside the Muckenhoupt Class. https://arxiv.org/abs/2606.31542

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