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

  1. Guadalupe, J.J. 1
  2. Pérez, M. 2
  3. Ruiz, F.J. 2
  4. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

Revista:
Constructive Approximation

ISSN: 0176-4276

Año de publicación: 1996

Volumen: 12

Número: 3

Páginas: 341-360

Tipo: Artículo

DOI: 10.1007/S003659900018 SCOPUS: 2-s2.0-0030493645 WoS: WOS:A1996VE50300003 arXiv: 9505214 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Constructive Approximation

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

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 Sn, their maximal operator S*, and the commutator [Mb, Sn], where Mb denotes the operator of pointwise multiplication by b ∈ BMO. We also prove some norm inequalities for Sn when ν is a sum of a Laguerre weight on R+ and a positive mass on 0.