Boundedness of the Hilbert Transform on Weighted Lorentz Spaces

  1. Agora, Elona
Supervised by:
  1. Javier Soria de Diego Director
  2. María Jesús Carro Rossell Director

Defence university: Universitat de Barcelona

Fecha de defensa: 13 July 2012

Committee:
  1. Francisco Javier Duoandikoetxea Zuazo Chair
  2. Joan Cerdà Martín Secretary
  3. Lubos Pick Committee member

Type: Thesis

Teseo: 348709 DIALNET lock_openTDX editor

Abstract

The main goal of this thesis is to characterize the weak-type (resp. strong-type) boundedness of the Hilbert transform H on weighted Lorentz spaces ?pu(w). The characterization is given in terms of some geometric conditions on the weights u and w and the weak-type (resp. strong-type) boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results extend and unify simultaneously the theory of the boundedness of H on weighted Lebesgue spaces Lp(u) and Muckenhoupt weights Ap, and the theory on classical Lorentz spaces ?p(w) and Ariño-Muckenhoupt weights Bp.