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We consider the interpolation inequality with respect to the regularity index 𝑠 ∈ R in homogeneous Besov spaces Ḃ^𝑠 _<𝑝,𝑞> (R^𝑛). By choosing a general summability index 1 ≤ q ≤ ∞ and estimating care...fully, we reveal a precise representation of the constant appearing in the interpolation inequality. As an application of the refined interpolation inequality, we show a generalization of the Gagliardo–Nirenberg inequality in homogeneous Besov spaces given by Wadade (2009).続きを見る
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