אריה קנטורוביץ

For x [0, 1]ⁿ with ₁ = 1 and y ∈ [1, ∞)ⁿ, we prove that $$\frac{\Vert\textit{\ textbf{xy}}\Vert-{\infty}}{\Vert\textit{\textbf{xy}}\Vert-{2}} \le \Vert\textit{\textbf{x}}\Vert-{\infty} \Vert\textit{\textbf{y}}\Vert-{1} \frac{\Vert\textit{\textbf{y}}\Vert-{\infty}}{\Vert\textit{\textbf{y}}\Vert-{2}} $$, where xy ⁿ is the vector with components x _iy_i. This bound does not seem to easily follow from known inequalities, and the proof technique may be of independent interest.