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

Fernando Albiac; José L. Ansorena; Óscar Ciaurri; Juan L. Varona

doi:10.4171/rmi/1062

JournalsrmiVol. 35, No. 2pp. 561–574

Unconditional and quasi-greedy bases in $L_{p}$ with applications to Jacobi polynomials Fourier series

Fernando Albiac
Universidad Pública de Navarra, Pamplona, Spain
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- zbMATH Open
José L. Ansorena
Universidad de la Rioja, Logroño, Spain
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- zbMATH Open
Óscar Ciaurri
Universidad de la Rioja, Logroño, Spain
- MathSciNet
- zbMATH Open
Juan L. Varona
Universidad de la Rioja, Logroño, Spain
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Abstract

We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in $L_{p}$ does not converge unless $p = 2$ . As a by-product of our work on quasi-greedy bases in $L_{p} (μ)$ , we show that no normalized unconditional basis in $L_{p}$ , $p \neq = 2$ , can be semi-normalized in $L_{q}$ for $q \neq = p$ , 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 $L_{p}$ with applications to Jacobi polynomials Fourier series. Rev. Mat. Iberoam. 35 (2019), no. 2, pp. 561–574

DOI 10.4171/RMI/1062