Vector-valued inequalities with weights

• Autores: José Luis Torrea Hernández , Luz M. Fernández-Cabrera Marín
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 37, Nº 1, 1993, págs. 177-208
• Idioma: inglés
• DOI: 10.5565/publmat_37193_13
• Títulos paralelos:
  • Desigualdades vector-valuadas con pesos
• Enlaces
  • Texto completo
• Resumen

  • This paper deals with the following problem:

    Let T be a given operator. Find conditions on v(x) (resp. u(x)) such that ? |Tf(x)|pu(x) dx = C ? |f(x)|pv(x) dx is satisfied for some u(x) (resp. v(x)).

    Using vector-valued inequalities the problem is solved for: Carleson's maximal operator of Fourier partial sums, Littlewood-Paley square functions, Hilbert transform of functions valued in U.M.D. Banach spaces and operators in the upper-half plane.