Weighted norm inequalities for polynomial expansions associated to some measures with mass points (original) (raw)
1996, Constructive Approximation
Fourier series in orthogonal polynomials with respect to a measure ν on [−1, 1] are studied when ν 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 ∈ BMO. We also prove some norm inequalities for S n when ν is a sum of a Laguerre weight on R + and a positive mass on 0.
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