Abstract
A variant of the Gagliardo–Nirenberg inequality in Hat–Sobolev spaces is proved, which improves certain classes of classical Sobolev embeddings. Some continuation criterion for the incompressible Navier–Stokes system is established as an application. A direct proof of the fractional Gagliardo–Nirenberg inequality in end-point Besov spaces is given and as a corollary, its counterpart in Fourier–Herz spaces is established.
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