In the field of mathematical analysis, an interpolation inequality is an inequality of the form ‖ u 0 ‖ 0 ≤ C ‖ u 1 ‖ 1 α 1 ‖ u 2 ‖ 2 α 2 … ‖ u n ‖ n α n, n ≥ 2, {\displaystyle \|u_{0}\|_{0}\leq C\|u_{1}\|_{1}^{\alpha _{1}}\|u_{2}\|_{2}^{\alpha _{2}}\dots \|u_{n}\|_{n}^{\alpha _{n}},\quad n\geq 2,} where for 0 ≤ k ≤ n {\displaystyle 0\leq k\leq n}, u k {\displaystyle u_{k}} is an element of some particular vector space X k {\displaystyle X_{k}} equipped with norm ‖ ⋅ ‖ k {\displaystyle \|\cdot \|_{k}} and α k {\displaystyle \alpha _{k}} is some real exponent, and C {\displaystyle C} is some constant independent of u 0, .. Wikipedia