 
Summary: On multivariable Fej´er inequalities
Linda J. Patton
Mathematics Department, Cal Poly,
San Luis Obispo, CA 93407
Mihai Putinar
Mathematics Department, University of California,
Santa Barbara, 93106
September 20, 2005
Abstract
A nonnegative pluriharmonic polynomial p(z) on the unit ball of Cn
is used as a weight against the rotationally invariant measure on the unit
sphere. The resulting Hardy space carries the canonical ntuple S of mul
tiplication by the coordinate functions. By means of compressions of S to
coanalytically invariant subspaces, and known estimates of the numerical
radius of a nilpotent matrix we obtain bounds for the coefficients of p, in
terms of the arithmetic mean and degree of p, and dimension n.
MSC 2000: 42B05, 47A12, 31C10
1 Introduction
The following remarkable inequality was discovered by Fej´er in 1910 and later
published in [4, 5].
