Representation of reproducing kernels and the Lebesgue constants on the ball

For the weight function (1 - parallel tox parallel to (2))(mu -1/2) on the unit ball, a closed formula of the reproducing kernel is modified to includ e the case -1/2 < mu < 0. The new formula is used to study the orthogonal p rojection of the weighted L-2 space onto the space of polynomials of degree at most n, and it is proved that the uniform norm of the projection operat or has the growth rate of for mu < 0, which is the smallest possible growth rate among all projections, while the rate for mu greater than or equal to 0 is n(mu+(d-1)/2). (C) 2001 Academic Press.