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arXiv · 1507.05934

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
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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 $L_{p}(\mu)$, 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.

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BibTeXRIS

Fernando Albiac, José L. Ansorena, Óscar Ciaurri, Juan L. Varona. 2015-07-21. Unconditional and quasi-greedy bases in $L_p$ with applications to Jacobi polynomials Fourier series. https://arxiv.org/abs/1507.05934

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