This is an announcement for the paper "Unconditional and quasi-greedy bases in $L_p$ with applications to Jacobi polynomials Fourier series" by Fernando Albiac, Jose L. Ansorena, Oscar Ciaurri and Juan L. Varona.
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 $L_{p}(\mu)$, we show that no normalized unconditional basis in $L_p$, $p\not=2$, can be semi-normalized in $L_q$ for $q\not=p$, thus extending a classical theorem of Kadets and Pe{\l}czy{'n}ski from 1968.
Archive classification: math.FA
Mathematics Subject Classification: 46B15 (Primary) 41A65 (Secondary)
Submitted from: joseluis.ansorena@unirioja.es
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1507.05934
or