Inconditional and quasi-greedy bases in Lp with applications to Jacobi polynomials Fourier series

  1. Fernando Albiac 1
  2. José L. Ansorena 2
  3. Óscar Ciaurri 2
  4. Juan L. Varona 2
  1. 1 Universidad Pública de Navarra
    info

    Universidad Pública de Navarra

    Pamplona, España

    ROR https://ror.org/02z0cah89

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Aldizkaria:
Revista matemática iberoamericana

ISSN: 0213-2230

Argitalpen urtea: 2019

Alea: 35

Zenbakia: 2

Orrialdeak: 561-574

Mota: Artikulua

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Laburpena

We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in Lp does not converge unless p=2. As a by-product of our work on quasi-greedy bases in Lp(μ), we show that no normalized unconditional basis in Lp, p≠2, can be semi-normalized in Lq for q≠p, thus extending a classical theorem of Kadets and Pełczyński from 1962.

Datuen iturria: Dialnet