Characterization of the restricted type spaces r(x) Articles uri icon

authors

  • SORIA, JAVIER
  • TRADACETE PEREZ, PEDRO

publication date

  • January 2015

start page

  • 295

end page

  • 319

issue

  • 1

volume

  • 18

International Standard Serial Number (ISSN)

  • 1331-4343

Electronic International Standard Serial Number (EISSN)

  • 1848-9966

abstract

  • We study functorial properties of the spaces R(X), which have been recently introduced as a central tool in the analysis of the Hardy operator minus the identity on decreasing functions. In particular, we provide conditions on a minimal Lorentz space.. so that the equation R(X) = Lambda(phi) has a solution within the category of rearrangement invariant (r.i.) spaces. Moreover, we show that f R(X) = Lambda(phi), then we can always take X to be the minimal r.i. Banach range space for the Hardy operator defined in Lambda(phi).