10 research outputs found

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

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    Fourier series in orthogonal polynomials with respect to a measure Îœ\nu on [−1,1][-1,1] are studied when Îœ\nu is a linear combination of a generalized Jacobi weight and finitely many Dirac deltas in [−1,1][-1,1]. We prove some weighted norm inequalities for the partial sum operators SnS_n, their maximal operator S∗S^* and the commutator [Mb,Sn][M_b, S_n], where MbM_b denotes the operator of pointwise multiplication by b \in \BMO. We also prove some norm inequalities for SnS_n when Îœ\nu is a sum of a Laguerre weight on R+\R^+ and a positive mass on 00
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