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

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

1995-05-31

arxiv.org/abs/math/9505214v1

Constr. Approx. 12 (1996), 341-360

Mathematics

Classical Analysis and ODEs

Scientific paper

10.1007/BF02433048

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 $0$.

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