Unconditional constants and polynomial inequalities |
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| Authors: | BC Grecu GA Muñoz-Fernández JB Seoane-Sepúlveda |
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| Institution: | aDepartment of Pure Mathematics, Queen’s University Belfast, Northern Ireland, UK;bDepartamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040, Madrid, Spain |
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| Abstract: | If P is a polynomial on Rm of degree at most n, given by  , and Pn(Rm) is the space of such polynomials, then we define the polynomial |P| by  . Now if  is a convex set, we define the norm  on Pn(Rm), and then we investigate the inequality  providing sharp estimates on  for some specific spaces of polynomials. These  ’s happen to be the unconditional constants of the canonical bases of the considered spaces. |
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| Keywords: | Unconditional constant Polynomial inequalities Trinomials Homogeneous polynomials Extreme points |
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