Explicit norm attaining polynomials (Q1418393)

The author describes the \(2\)-homogeneous polynomials attaining in the norm at a certain point of the unit sphere of \(({\mathbb{R}}^2, \| \;\|)\), where \(\| \;\| \) is the \(\ell_1\)-norm, the Euclidian or the maximum norm. The results of previous papers that characterize norm one polynomials on \(({\mathbb{R}}^2, \| \;\| _1)\) or \(({\mathbb{R}}^2, \| \;\| _2)\) are used [see J. Math. Anal. Appl. 228, No. 2, 467--482 (1998; Zbl 0922.46042) and Arch. Math. 71, No. 6, 472--480 (1998; Zbl 0937.46043)].