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We consider embeddings of a class of fractional Sobolev spaces E s (Ω) (s ≥ 0) into their limiting L p (Ω) spaces, for a bounded smooth domain Ω ⊂ ℝ N , and study the relationship between the best constants for these embeddings and other best constants corresponding to the case Ω = ℝ N .

On Best Constants for Limiting Embeddings of Fractional Sobolev Spaces