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arXiv · 2503.14636

Complex interpolation of power-weighted Sobolev spaces with boundary conditions

Floris B. Roodenburg
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Abstract

We characterise the complex interpolation spaces of weighted vector-valued Sobolev spaces with and without boundary conditions on the half-space and on smooth bounded domains. The weights we consider are power weights that measure the distance to the boundary and do not necessarily belong to the class of Muckenhoupt $A_p$ weights. First, we determine the higher-order trace spaces for weighted vector-valued Besov, Triebel-Lizorkin, Bessel potential and Sobolev spaces. This allows us to derive a trace theorem for boundary operators and to interpolate spaces with boundary conditions. Furthermore, we derive density results for weighted Sobolev spaces with boundary conditions.

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Floris B. Roodenburg. 2025-03-18. Complex interpolation of power-weighted Sobolev spaces with boundary conditions. https://arxiv.org/abs/2503.14636

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