WEIGHTED NORM INEQUALITIES FOR POLYNOMIAL-EXPANSIONS ASSOCIATED TO SOME MEASURES WITH MASS POINTS

Fourier series in orthogonal polynomials with respect to a measure nu on [-1, 1] are studied when nu is a linear combination of a generalize d Jacobi weight and finitely many Dirac deltas in [-1, 1]. We prove so me weighted norm inequalities for the partial sum operators S-n, their maximal operator S, and the commutator [M(b), S-n], where M(b) denot es the operator of pointwise multiplication by b epsilon BMO. We also prove some norm inequalities for S-n when nu is a sum of a Laguerre we ight on R(+) and a positive mass on 0.