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

• Fernando Albiac ^[1] ; José L. Ansorena ^[2] ; Óscar Ciaurri ^[2] ; Juan L. Varona ^[2]
  1. [1] Universidad Pública de Navarra

     Universidad Pública de Navarra

     Pamplona, España

     
  2. [2] Universidad de La Rioja

     Universidad de La Rioja

     Logroño, España

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 2, 2019, págs. 561-574
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.