A number of sharp inequalities are proved for the space P (2D (π/4)) of 2-homogeneous polynomials on ℝ2 endowed with the supremum norm on the sector D (π/4) := {eiθ : θ ∈ [0, π/4]}. Among the main results we can find sharp Bernstein and Markov inequalities and the calculation of the polarization constant and the unconditional constant of the canonical basis of the space P (2D (π/4)).
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