Endpoint multiplier theorems of Marcinkiewicz type

  • Terence Tao

    University of California Los Angeles, United States
  • James Wright

    University of Edinburgh, UK


We establish sharp (H1,L1,q)(H^1, L^{1,q}) and local (LL logrL,L1,q^r L, L^{1,q}) mapping properties for rough one-dimensional multipliers. In particular we show that the multipliers in the Marcinkiewicz multiplier theorem map H1H^1 to L1,L^{1,\infty} and LL log1/2L^{1/2}L to L1,L^{1,\infty}, and that these estimates are sharp.

Cite this article

Terence Tao, James Wright, Endpoint multiplier theorems of Marcinkiewicz type. Rev. Mat. Iberoam. 17 (2001), no. 3, pp. 521–558

DOI 10.4171/RMI/303