Weighted norm inequalities for polynomial expansions associated to some measures with mass points

Abstract

Fourier series in orthogonal polynomials with respect to a measure $\nu$ on $[-1,1]$ are studied when $\nu$ is a linear combination of a generalized Jacobi weight and finitely many Dirac deltas in $[-1,1]$. We prove some weighted norm inequalities for the partial sum operators $S_n$, their maximal operator $S^*$ and the commutator $[M_b, S_n]$, where $M_b$ denotes the operator of pointwise multiplication by $b \in \BMO$. We also prove some norm inequalities for $S_n$ when $\nu$ is a sum of a Laguerre weight on $\R^+$ and a positive mass on $0$.