Year: 2026
Type: article
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 Ap 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.
Source: Studia Mathematica
Author: Floris B. Roodenburg
Institution: Delft University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4414901211
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