Interpolation inequalities in Besov spaces

By Shuji Machihara, Tohru Ozawa. 2002

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On the asymptotic behavior of solution for the generalized IBq equation with hydrodynamical damped term (2012, unknown): “From Corollary 2 in [17] we see that ‖u0‖L2 ‖u0‖ s s+2γ +n/q−n/2 Ḣ −2γ 1 ‖u0‖ 2γ +n/q−n/2 s+2γ +n/q−n/2 Ḣ s is valid for all u0 ∈ Ḣ−2γ q ∩ Ḣ s .”
Necessary and Sucient Conditions for the Fractional Gagliardo-Nirenberg Inequalities and Applications to Navier-Stokes and Generalized Boson Equations (2011, background): “3 below cover all of the available GN inequalities in [5, 9, 10, 15, 16, 17, 22, 25, 29, 30, 38, 42, 50, 52, 55] for both integer and fractional versions.”
Gagliardo–Nirenberg Inequalities with a BMO Term (2006, background): “For related interpolation inequalities, see for instance [3], [4], [9], and [10].”
Necessary and Sufficient Conditions for the Fractional Gagliardo-Nirenberg Inequalities and Applications to Navier-Stokes and Generalized Boson Equations (Harmonic Analysis and Nonlinear Partial Differential Equations) (2011, background): “Machihara and Ozawa [42] showed that Proposition 3.”