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Some new light on a few classical results

Volume 140 / 2015

Ciprian Demeter, Prabath Silva Colloquium Mathematicum 140 (2015), 129-147 MSC: Primary 42B20; Secondary 42B25. DOI: 10.4064/cm140-1-11

Abstract

The purpose of this paper is to describe a unified approach to proving vector-valued inequalities without relying on the full strength of weighted theory. Our applications include the Fefferman–Stein and Córdoba–Fefferman inequalities, as well as the vector-valued Carleson operator. Using this approach we also produce a proof of the boundedness of the classical bi-parameter multiplier operators, which does not rely on product theory. Our arguments are inspired by the vector-valued restricted type interpolation used by Bateman and Thiele (2013).

Authors

  • Ciprian DemeterDepartment of Mathematics
    Indiana University
    831 East 3rd St.
    Bloomington, IN 47405, U.S.A.
    e-mail
  • Prabath SilvaDepartment of Mathematics
    California Institute of Technology
    Mathematics 253-37, Caltech
    Pasadena, CA 91125, U.S.A.
    e-mail

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