JournalsrmiVol. 35, No. 2pp. 561–574

Unconditional and quasi-greedy bases in LpL_p with applications to Jacobi polynomials Fourier series

  • Fernando Albiac

    Universidad Pública de Navarra, Pamplona, Spain
  • José L. Ansorena

    Universidad de la Rioja, Logroño, Spain
  • Óscar Ciaurri

    Universidad de la Rioja, Logroño, Spain
  • Juan L. Varona

    Universidad de la Rioja, Logroño, Spain
Unconditional and quasi-greedy bases in $L_p$ with applications to Jacobi polynomials Fourier series cover
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Abstract

We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in LpL_p does not converge unless p=2p = 2. As a by-product of our work on quasi-greedy bases in Lp(μ)L_p(\mu), we show that no normalized unconditional basis in LpL_p, p2p \neq 2, can be semi-normalized in LqL_q for qpq \neq p, thus extending a classical theorem of Kadets and Pełczyński from 1962.

Cite this article

Fernando Albiac, José L. Ansorena, Óscar Ciaurri, Juan L. Varona, Unconditional and quasi-greedy bases in LpL_p with applications to Jacobi polynomials Fourier series. Rev. Mat. Iberoam. 35 (2019), no. 2, pp. 561–574

DOI 10.4171/RMI/1062