Interpolation inequalities between Lorentz space and BMO: the endpoint case (L^{1,infinity}, BMO)

Abstract

We prove interpolation inequalities by means of the Lorentz norm, BMO norm, and the fractional Sobolev norm. In particular, we obtain an interpolation inequality for $(L^{1,\infty}, BMO)$, that we call the endpoint case.

Keywords

• Gagliardo-Nirenberg inequality
• Lorentz spaces
• BMO space
• Fractional Sobolev spaces