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  • On pointwise a.e. convergence of multilinear operators

  • Part of
  • Loukas Grafakos, Danqing He, Petr Honzík, Bae Jun Park
  • Journal:
    Canadian Journal of Mathematics / Volume 76 / Issue 3 / June 2024
    Published online by Cambridge University Press:
    29 May 2023, pp. 1005-1032
    Print publication:
    June 2024
    • Article
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  • In this work, we obtain the pointwise almost everywhere convergence for two families of multilinear operators: (a) the doubly truncated homogeneous singular integral operators associated with $L^q$ functions on the sphere and (b) lacunary multiplier operators of limited smoothness. The a.e. convergence is deduced from the $L^2\times \cdots \times L^2\to L^{2/m}$ boundedness of the associated maximal multilinear operators.