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Abstract

We consider the interpolation inequality with respect to the regularity index $s \in R$ in homogeneous Besov spaces ${\dot{B}}_{p, q}^{s} (R^{n})$ . By choosing a general summability index $1 \leq q \leq \infty$ and estimating carefully, 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).

Keywords

interpolation inequality Gagliardo–Nirenberg inequality homogeneous Besov spaces divergence rates

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Refined Interpolation Inequality in Besov Spaces With Applications to the Gagliardo–Nirenberg Inequality

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