Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 21 (2014), No. 3, 745--764Copyright Heldermann Verlag 2014 Supremum Norms for 2-Homogeneous Polynomials on Circle Sectors Gustavo A. Muñoz-Fernández Dep. de Análisis Matemático, Universidad Complutense de Madrid, Plaza Ciencias 3, 28040 Madrid, Spain gustavo_fernandez@mat.ucm.es Daniel Pellegrino Dep. de Matemática,, Universidade Federal da Paraíba, 58.051-900 - João Pessoa, Brazil pellegrino@pq.cnpq.br Juan B. Seoane-Sepúlveda Dep. de Análisis Matemático, Universidad Complutense de Madrid, Plaza Ciencias 3, 28040 Madrid, Spain jseoane@mat.ucm.es Andreas Weber Institut für Algebra und Geometrie, Karlsruher Institut für Technologie, Kaiserstr. 89-93, 76128 Karlsruhe, Germany andreasweber.mail@gmail.com [Abstract-pdf] We consider the Banach space of two homogeneous polynomials endowed with the supremum norm $\|\cdot\|_{D(\beta)}$ over circle sectors $D(\beta)$ of angle $\beta$ for several values of $\beta\in[0,2\pi]$. We provide an explicit formula for $\|\cdot\|_{D(\beta)}$, 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. Keywords: Bernstein and Markov inequalities, unconditional constants, polarizations constants, polynomial inequalities, homogeneous polynomials, extreme points. MSC: 46G25; 46B28, 41A44 [ Fulltext-pdf  (1449  KB)] for subscribers only.