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00925njm 22002777a 4500 dc Grecu, B.C. author Muñoz-Fernández, Gustavo A. author Seoane Sepúlveda, Juan Benigno author 2009-12 If P is a polynomial on R of degree at most n, given by P(x) = Sigma(alpha is an element of Nm,vertical bar alpha vertical bar <= n) a(alpha)x(alpha), and P(n)(R(m)) is the space of such polynomials, then we define the polynomial vertical bar P vertical bar by vertical bar P vertical bar(x) = Sigma(alpha is an element of Nm,vertical bar alpha vertical bar <= n) vertical bar a(alpha vertical bar)x(alpha). Now if B subset of R(m) is a convex set, we define the norm parallel to P parallel to(B) := sup{vertical bar(x)vertical bar : x is an element of B} on P(n)(R(m)), and then we investigate the inequality vertical bar vertical bar vertical bar P vertical bar vertical bar vertical bar(B) <= C(B)vertical bar vertical bar vertical bar P vertical bar vertical bar vertical bar(B), providing sharp estimates on C(B) for some specific spaces of polynomials. These C(B)'s happen to be the unconditional constants of the canonical bases of the considered spaces. 0021-9045 10.1016/j.jat.2008.12.001 https://hdl.handle.net/20.500.14352/42379 http://www.sciencedirect.com/science/article/pii/S002190450800258X http://www.sciencedirect.com/ Unconditional constants and polynomial inequalities