Endpoint estimates from restricted rearrangement inequalities

  • María Belén J. Carro

    Universitat de Barcelona, Spain
  • Joaquim Martín

    Universitat Autònoma de Barcelona, Bellaterra, Spain


Let TT be a sublinear operator such that (Tf)(t)h(t,f1)(Tf)^*(t)\le h(t, \|f\|_1) for some positive function h(t,s)h(t,s) and every function ff such that f1\|f\|_{\infty}\le 1. Then, we show that TT can be extended continuously from a logarithmic type space into a weighted weak Lorentz space. This type of result is connected with the theory of restricted weak type extrapolation and extends a recent result of Arias-de-Reyna concerning the pointwise convergence of Fourier series to a much more general context.

Cite this article

María Belén J. Carro, Joaquim Martín, Endpoint estimates from restricted rearrangement inequalities. Rev. Mat. Iberoam. 20 (2004), no. 1, pp. 131–150

DOI 10.4171/RMI/383