Continuous interpolation spaces with a function parameter : Properties and applications

This paper investigates continuous interpolation spaces defined by a function parameter, a construct central to the theory of traces and the analysis of boundary value problems for partial differential equations. We explore their functorial interpretation and establish density results for specific cases. These spaces, characterized by asymptotic regularity properties, are instrumental in the analysis of operators in weighted functional spaces and in solving PDEs with precise boundary behavior. The paper also addresses limiting cases, θ = 0 and θ = 1, in the definitions of Kθ∞ and Jθ∞. As illustrated, these techniques, when applied to traditional spaces, can give rise to new spaces.