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We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in does not converge unless . As a by-product of our work on quasi-greedy bases in , we show that no normalized unconditional basis in , , can be semi-normalized in for , thus extending a classical theorem of Kadets and Pełczyński from 1962.
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Fernando Albiac, José L. Ansorena, Óscar Ciaurri, Juan L. Varona, Unconditional and quasi-greedy bases in with applications to Jacobi polynomials Fourier series. Rev. Mat. Iberoam. 35 (2019), no. 2, pp. 561–574DOI 10.4171/RMI/1062