Convergencia en Lp con pesos de la Serie de Fourier respecto de algunos sistemas ortogonales

  1. Varona Malumbres, Juan Luis
Supervised by:
  1. José Javier Guadalupe Hernández Director

Defence university: Universidad de Cantabria

Year of defence: 1988

Committee:
  1. José Manuel Bayod Bayod Chair
  2. Francisco José Ruiz Blasco Secretary
  3. José Manuel Carreas Dobato Committee member
  4. Miguel Lobo Hidalgo Committee member
  5. Francisco Marcellán Español Committee member

Type: Thesis

Teseo: 22339 DIALNET lock_openDialnet editor
Institutional repository: lock_openOpen access Postprint lock_openOpen access Editor

Abstract

Convergence of the fourier series with respect to several orthogonal systems abstract. Given an orthogonal complete system with respect to a measure µ on an interval, we approach the convergence in weighted Lp spaces of the corresponding Fourier series. The orthogonal systems we analyze are generalized Jacobi, generalized Hermite, several systems of orthogonal polynomials with respect to weights with Dirac's deltas and Bessel and Dini's systems. In this study we use good estimates of the orthonormal functions and results on Ap-theory in order to solve the boundedness of the Hilbert transform with one or two weights.