For homogeneous polynomials 
and 
of degree 
and 
, then
![sqrt((m!n!)/((m+n)!))[P]_2[Q]_2<=[P·Q]_2<=[P]_2[Q]_2,](/images/equations/BombierisInequality/NumberedEquation1.svg) |
where ![[P·Q]_2](/images/equations/BombierisInequality/Inline5.svg)
is the Bombieri norm.
Bombieri's Inequality
See also
Beauzamy and Dégot's Identity, Bombieri Norm, Boundedly Compact Space, Reznick's IdentityExplore with Wolfram|Alpha
References
Borwein, P. and Erdélyi, T. "Bombieri's Norm." §5.3.E.7 in Polynomials and Polynomial Inequalities. New York: Springer-Verlag, p. 274, 1995.Referenced on Wolfram|Alpha
Bombieri's InequalityCite this as:
Weisstein, Eric W. "Bombieri's Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BombierisInequality.html