If P(z) be a polynomial of degree at most n which does not vanish in β£zβ£<1, it was recently formulated by Shah and Liman \cite[\textit{Integral
estimates for the family of B-operators, Operators and Matrices,}
\textbf{5}(2011), 79 - 87]{wl} that for every Rβ₯1, pβ₯1,
β₯B[PβΟ](z)β₯pββ€β₯1+zβ₯pβRnβ£Ξnββ£+β£Ξ»0ββ£ββ₯P(z)β₯pβ,
where B is a Bnβ-operator with parameters Ξ»0β,Ξ»1β,Ξ»2β in the sense of Rahman \cite{qir}, Ο(z)=Rz and
Ξnβ=Ξ»0β+Ξ»1β2n2β+Ξ»2β8n3(nβ1)β. Unfortunately the proof of this result is
not correct. In this paper, we present a more general sharp Lpβ-inequalities
for Bnβ-operators which not only provide a correct proof of the
above inequality as a special case but also extend them for 0β€p<1 as
well.Comment: 16 Page