AN INEQUALITY INVOLVING THE ℓ1, ℓ2, AND ℓ∞ NORMS
Aryeh Kontorovich · Analysis and Applications · 2013
For x ∈ [0, 1]n with ‖x‖1 = 1 and y ∈ [1, ∞)n, we prove that [Formula: see text] where xy ∈ ℝn is the vector with components xiyi. This bound does not seem to easily follow from known inequalities, and the proof technique may be of independent interest.