Endpoint estimates from restricted rearrangement inequalities

María J. Carro, Joaquim Martín

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)

Abstract

Let T be a sublinear operator such that (Tf)*(t) ≤ h(t,∥f∥ 1 ) for some positive function h(t, s) and every function / such that ∥f∥ ∞ ≤ 1. Then, we show that T 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.
Original languageEnglish
Pages (from-to)131-150
JournalRevista Matematica Iberoamericana
Volume20
Issue number1
DOIs
Publication statusPublished - 1 Jan 2004

Keywords

  • Banach couples
  • Carleson's operator
  • Extrapolation theory
  • Real interpolation
  • Rearrangement inequality

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