| Abstract: |
| Function spaces measuring size and smoothness, such as Sobolev spaces, Besov spaces, and Triebel--Lizorkin spaces, naturally materialize in the formulation of boundary value problems and it has been particularly important, in this regard, to fully understand the fundamental properties of these function spaces in very general geometric settings. In this talk we will survey some recently obtained results pertaining to the extension and embedding properties for certain brands of these function spaces and we will highlight how the geometric makeup of the underlying ambient space directly influences the very nature of these function spaces (in a quantitative manner). |
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