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Resumen de Inconditional and quasi-greedy bases in Lp with applications to Jacobi polynomials Fourier series

Fernando José Albiac Alesanco Árbol académico, José Luis Ansorena Barasoain Árbol académico, Óscar Ciaurri Ramírez Árbol académico, Juan Luis Varona Malumbres Árbol académico

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

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