Gagliardo-nirenberg Type Inequalities in Some Q−spaces
نویسندگان
چکیده
Abstract. In this paper, from a John-Nirenberg (JN) type inequality in BMO(R), we prove Gagliardo-Nirenberg (GN) type inequalities in Qα(R ) which mean the continuous embeddings L(R)∩Qα(R ) ⊆ L(R) for −∞ < α < β, 1/2 < β ≤ 1 and 2 ≤ r ≤ p < ∞. This result generalizes some known embeddings and implies the bilinear estimates in BMO(R) which are useful for studying Navier-Stokes equations. Meanwhile, from GN type inequalities in Qα(R ), we get Brezis-Gallouet-Wainger and Trudinger-Moser type inequalities which imply the equivalence of JN and GN type inequalities in BMO(R).
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