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Littlewood–Paley characterizations of fractional Sobolev spaces via averages on balls
By invoking some new ideas, we characterize Sobolev spaces W α,p (ℝ n ) with the smoothness order α ∊ (0, 2] and p ∊ (max{1, 2 n/ (2 α + n )}, ∞ ), via the Lusin area function and the Littlewood–Paley g* λ -function in terms of centred …