Resumen de Variants of the Calderón-Zygmund Theory for Lp-spaces.

Anthony Carbery

• The purposes of this paper may be described as follows:

  (i) to provide a useful substitute for the Cotlar-Stein lemma for Lp-spaces (the orthogonality conditions are replaced by certain fairly weak smoothness asumptions);

  (ii) to investigate the gap between the Hörmander multiplier theorem and the Littman-McCarthy-Rivière example - just how little regularity is really needed? (iii) to simplify and extend the work of Duoandikoetxea and Rubio de Francia and Christ and Stein, which sometimes has unnecessarily strong assumptions, and to introduce a sensitivity to different Lp-spaces which does not appear in their work.