JournalsrmiVol. 31, No. 2pp. 609–616

Multilinear paraproducts revisited

  • Loukas Grafakos

    University of Missouri, Columbia, USA
  • Danqing He

    University of Missouri, Columbia, USA
  • Nigel Kalton

    University of Missouri, Columbia, USA
  • Mieczysław Mastyło

    Adam Mickiewicz University, Poznan, Poland
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Abstract

We prove that multilinear paraproducts are bounded from products of Lebesgue spaces Lp1 ⁣××Lpm+1L^{p_1}\!\times \cdots \times L^{p_{m+1}} to Lp,L^{p,\infty}, when 1 ⁣p1,,pm1\le\! p_1, \dots , p_m, pm+1<p_{m+1}<\infty, 1/p1++1/pm+1=1/p1/p_1+\cdots +1/p_{m+1}=1/p. We focus on the endpoint case when some indices pjp_j are equal to 11, in particular we obtain a new proof of the estimate L1××L1L1/(m+1),L^1\times \cdots \times L^1\to L^{1/(m+1),\infty}.

Cite this article

Loukas Grafakos, Danqing He, Nigel Kalton, Mieczysław Mastyło, Multilinear paraproducts revisited. Rev. Mat. Iberoam. 31 (2015), no. 2, pp. 609–616

DOI 10.4171/RMI/847