Let be a sublinear operator such that for some positive function and every function such that . Then, we show that 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. 131–150DOI 10.4171/RMI/383