A lacuna in the functional 𝐿_{𝑝}-Busemann-Petty centroid inequality

We extend the study of the functional <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Subscript p"> <mml:semantics> <mml:msub> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">L_p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -Busemann-Petty centroid inequality by addressing an endpoint case, complementing the results of Haddad et al. [Int. Math. Res. Not. IMRN 10 (2021), pp. 7947–7965].