Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors

We consider the Banach space of two homogeneous polynomials endowed with the supremum norm

over circle sectors

D(\beta) D ( β )

of angle

\beta β

for several values of

\beta\in[0,2\pi] β ∈ [ 0 , 2 π ]

. We provide an explicit formula for

\|\cdot\|_{D(\beta)} ∥ ⋅ ∥ D ( β )

, a full description of the extreme points of the corresponding unit balls, and a parametrization and a plot of their unit spheres. This work is an extension of a series of papers on the same topic published in the last decade and it has a number of applications to obtain polynomial-type inequalities.