Extended Sobolev Scale on Non-Compact Manifolds

2025/09/24 by Milatovic, Ognjen
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.20598

Abstract

Adapting the definition of ``extended Sobolev scale" on compact manifolds by Mikhailets and Murach to the setting of a (generally non-compact) manifold of bounded geometry X, we define the ``extended Sobolev scale" H^φ(X), where φ is a function which is RO-varying at infinity. With the help of the scale H^φ(X), we obtain a description of all Hilbert function-spaces that serve as interpolation spaces with respect to a pair of Sobolev spaces [H^(s₀)(X), H^(s₁)(X)], with s₀

Citations

• Extended Sobolev scale for vector bundles, and its applications
• Parabolic boundary-value problems and generalized Sobolev spaces
• An extended Hilbert scale and its applications
• Parabolic problems in generalized Sobolev spaces
• K-homology classes of elliptic uniform pseudodifferential operators
• Hörmander Spaces, Interpolation, and Elliptic Problems

Related

• Extended Sobolev Scale on ℤⁿ
• Extended Sobolev scale for vector bundles, and its applications
• An extended Hilbert scale and its applications
• Sobolev spaces in extended metric-measure spaces
• A Bourgain-Gromov problem on non-compact Sobolev-Lorentz embeddings