  In this work we obtain the pointwise almost everywhere convergence for two
families of multilinear operators: (a) truncated homogeneous singular integral
operators associated with $L^q$ functions on the sphere and (b) lacunary
multiplier operators of limited decay.
  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.
